{"id":262,"date":"2023-06-08T14:25:42","date_gmt":"2023-06-08T14:25:42","guid":{"rendered":"https:\/\/ilm.com.pk\/online-test\/?p=262"},"modified":"2023-06-08T09:21:57","modified_gmt":"2023-06-08T09:21:57","slug":"2nd-year-math-chapter-7-vectors-mcqs-with-answers","status":"publish","type":"post","link":"https:\/\/ilm.com.pk\/online-test\/2nd-year-math-chapter-7-vectors-mcqs-with-answers\/","title":{"rendered":"2nd Year Math Chapter 7 Vectors MCQs With Answers"},"content":{"rendered":"<p style=\"text-align: justify;\">You can get the important 2nd Year Math Chapter 7 Vectors MCQs With Answers here. This is the last chapter of 2nd-year Maths and is the most important one. There are some important concepts in this chapter including the introduction of vectors and scalars, types of vectors, the ratio formula, the Introduction of vectors in space, the scalar product of two vectors, the vector product of two vectors, and the scalar triple product of vectors. So, in order to prepare for these important topics, these MCQs will give you good help. These 2nd Year Maths Chapter 7 MCQs will help you to check the important MCQs and hence they are very important. Here below, there is a quiz given. After solving the quiz, you can check the answers that will help you to improve the mistakes. So, let&#8217;s check the MCQs.<\/p>\n<h2 style=\"text-align: center;\">2nd Year Math Chapter 7 Vectors MCQs With Answers<\/h2>\n<div class='ays-quiz-wrap'>\n            <div class='ays-quiz-container ays_quiz_elegant_light  '\n                 data-quest-effect='shake' \n                 data-hide-bg-image='false'\n                 id='ays-quiz-container-79'>\n                <div class='ays-live-bar-wrap '><div class='ays-live-bar-fill ' style='width: 0%;'><span><span class='ays-live-bar-percent'>0<\/span>%<\/span><\/div><\/div>\n                \n                <div class='ays-questions-container'>\n                    <div class='ays-quiz-some-items-icons-wrap'><\/div>\n                    <span class='ays_quizn_ancnoxneri_qanak'><i class='ays_fa ays_fa_users'><\/i> 647<\/span>\n                    <div id='ays-quiz-questions-nav-wrap-79' class='ays-quiz-questions-nav-wrap'><div class='ays-quiz-questions-nav-go-left'>\n                    <i class='ays_fa ays_fa_angle_left'><\/i>\n                <\/div><div class='ays-quiz-questions-nav-go-right'>\n                    <i class='ays_fa ays_fa_angle_right'><\/i>\n                <\/div><div class='ays-quiz-questions-nav-content'><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1640' class='ays_questions_nav_question'>1<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1635' class='ays_questions_nav_question'>2<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1630' class='ays_questions_nav_question'>3<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1641' class='ays_questions_nav_question'>4<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1627' class='ays_questions_nav_question'>5<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1634' class='ays_questions_nav_question'>6<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1633' class='ays_questions_nav_question'>7<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1624' class='ays_questions_nav_question'>8<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1632' class='ays_questions_nav_question'>9<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1626' class='ays_questions_nav_question'>10<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1637' class='ays_questions_nav_question'>11<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1629' class='ays_questions_nav_question'>12<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1631' class='ays_questions_nav_question'>13<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1643' class='ays_questions_nav_question'>14<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1625' class='ays_questions_nav_question'>15<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1642' class='ays_questions_nav_question'>16<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1628' class='ays_questions_nav_question'>17<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1636' class='ays_questions_nav_question'>18<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1638' class='ays_questions_nav_question'>19<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1639' class='ays_questions_nav_question'>20<\/a><\/div><\/div><\/div>\n                    <form \n                        action='' \n                        method='post' \n                        autocomplete='off'\n                        id='ays_finish_quiz_79' \n                        class=' enable_questions_result '\n                    >\n            <input type='hidden' value='list' class='answer_view_class'>\n            <input type='hidden' value='' class='ays_qm_enable_arrows'><section  style='display:none;'  class='ays_quiz_timer_container'>\n                <div class='ays-quiz-timer ' data-timer='100'><\/div>\n                <div class='ays-quiz-after-timer  empty_after_timer_text '><\/div>\n                <hr style='height:1px;'>\n            <\/section>\n            \n            <div class='step active-step'>\n                <div class='ays-abs-fs ays-start-page'>\n                    \n                    \n                    <p class='ays-fs-title'>2nd Year Math Chapter 7<\/p>\n                    \n                    <input type='hidden' name='ays_quiz_id' value='79'\/>\n                    <input type='hidden' name='ays_quiz_questions' value='1643,1642,1641,1640,1639,1638,1637,1636,1635,1634,1633,1632,1631,1630,1629,1628,1627,1626,1625,1624'>\n                    \n                    <div class='ays_buttons_div'>\n                        <input type='button'   name='next' class='ays_next start_button action-button' value='Start' data-enable-leave-page=\"false\" \/>\n                    <\/div>\n                    \n                    \n                <\/div>\n            <\/div><div class='step  '\n                        data-question-id='1640'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>1 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>1. <strong>In space the vector j can be written as<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1640]' id='ays-answer-6351-79' value='6351'\/>\n\n                    <label for='ays-answer-6351-79' class='  ays_position_initial '>\n                        A) (1,0,0)\n                    <\/label>\n                    <label for='ays-answer-6351-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1640]' id='ays-answer-6354-79' value='6354'\/>\n\n                    <label for='ays-answer-6354-79' class='  ays_position_initial '>\n                        B) (1,0)\n                    <\/label>\n                    <label for='ays-answer-6354-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1640]' id='ays-answer-6352-79' value='6352'\/>\n\n                    <label for='ays-answer-6352-79' class='  ays_position_initial '>\n                        C) (0,1,0)\n                    <\/label>\n                    <label for='ays-answer-6352-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1640]' id='ays-answer-6353-79' value='6353'\/>\n\n                    <label for='ays-answer-6353-79' class='  ays_position_initial '>\n                        D) (0,0,1)\n                    <\/label>\n                    <label for='ays-answer-6353-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1635'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>2 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>2. <strong>If u = 3i \u2212 j + 2k then [3,-1,2] are called ____________ of u .<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1635]' id='ays-answer-6332-79' value='6332'\/>\n\n                    <label for='ays-answer-6332-79' class='  ays_position_initial '>\n                        A) direction ratios\n                    <\/label>\n                    <label for='ays-answer-6332-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1635]' id='ays-answer-6334-79' value='6334'\/>\n\n                    <label for='ays-answer-6334-79' class='  ays_position_initial '>\n                        B) elements\n                    <\/label>\n                    <label for='ays-answer-6334-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1635]' id='ays-answer-6333-79' value='6333'\/>\n\n                    <label for='ays-answer-6333-79' class='  ays_position_initial '>\n                        C) direction angles\n                    <\/label>\n                    <label for='ays-answer-6333-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1635]' id='ays-answer-6331-79' value='6331'\/>\n\n                    <label for='ays-answer-6331-79' class='  ays_position_initial '>\n                        D) Direction cosines\n                    <\/label>\n                    <label for='ays-answer-6331-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1630'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>3 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>3. <strong>If \u03b8 is the angle between two vectors a and b, then cos\u03b8 =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1630]' id='ays-answer-6312-79' value='6312'\/>\n\n                    <label for='ays-answer-6312-79' class='  ays_position_initial '>\n                        A) a.b\/|a||b|\n                    <\/label>\n                    <label for='ays-answer-6312-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1630]' id='ays-answer-6313-79' value='6313'\/>\n\n                    <label for='ays-answer-6313-79' class='  ays_position_initial '>\n                        B) a.b\/|a|\n                    <\/label>\n                    <label for='ays-answer-6313-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1630]' id='ays-answer-6314-79' value='6314'\/>\n\n                    <label for='ays-answer-6314-79' class='  ays_position_initial '>\n                        C) a.b\/|b|\n                    <\/label>\n                    <label for='ays-answer-6314-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1630]' id='ays-answer-6311-79' value='6311'\/>\n\n                    <label for='ays-answer-6311-79' class='  ays_position_initial '>\n                        D) a\u00d7b\/|a||b|\u00a0\n                    <\/label>\n                    <label for='ays-answer-6311-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1641'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>4 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>4. <strong>In space the vector i can be written as<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1641]' id='ays-answer-6357-79' value='6357'\/>\n\n                    <label for='ays-answer-6357-79' class='  ays_position_initial '>\n                        A) (0,0,1)\n                    <\/label>\n                    <label for='ays-answer-6357-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1641]' id='ays-answer-6355-79' value='6355'\/>\n\n                    <label for='ays-answer-6355-79' class='  ays_position_initial '>\n                        B) (1,0,0)\n                    <\/label>\n                    <label for='ays-answer-6355-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1641]' id='ays-answer-6356-79' value='6356'\/>\n\n                    <label for='ays-answer-6356-79' class='  ays_position_initial '>\n                        C) (0,1,0)\n                    <\/label>\n                    <label for='ays-answer-6356-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1641]' id='ays-answer-6358-79' value='6358'\/>\n\n                    <label for='ays-answer-6358-79' class='  ays_position_initial '>\n                        D) (1,0)\n                    <\/label>\n                    <label for='ays-answer-6358-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1627'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>5 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>5. <strong>Parallelogram law of vector addition to describe the combined action of two forces, was used by<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1627]' id='ays-answer-6301-79' value='6301'\/>\n\n                    <label for='ays-answer-6301-79' class='  ays_position_initial '>\n                        A) Alkhwarzmi\n                    <\/label>\n                    <label for='ays-answer-6301-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1627]' id='ays-answer-6299-79' value='6299'\/>\n\n                    <label for='ays-answer-6299-79' class='  ays_position_initial '>\n                        B) Cauchy\n                    <\/label>\n                    <label for='ays-answer-6299-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1627]' id='ays-answer-6300-79' value='6300'\/>\n\n                    <label for='ays-answer-6300-79' class='  ays_position_initial '>\n                        C) Aristotle\n                    <\/label>\n                    <label for='ays-answer-6300-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1627]' id='ays-answer-6302-79' value='6302'\/>\n\n                    <label for='ays-answer-6302-79' class='  ays_position_initial '>\n                        D) Leibnitz\n                    <\/label>\n                    <label for='ays-answer-6302-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1634'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>6 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">6. <b>Which of the following can be the direction angles of some vector<\/b><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1634]' id='ays-answer-6328-79' value='6328'\/>\n\n                    <label for='ays-answer-6328-79' class='  ays_position_initial '>\n                        A) 30\u00b0, 45\u00b0, 60\u00b0\n                    <\/label>\n                    <label for='ays-answer-6328-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1634]' id='ays-answer-6329-79' value='6329'\/>\n\n                    <label for='ays-answer-6329-79' class='  ays_position_initial '>\n                        B) 45\u00b0, 60\u00b0, 60\u00b0\n                    <\/label>\n                    <label for='ays-answer-6329-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1634]' id='ays-answer-6330-79' value='6330'\/>\n\n                    <label for='ays-answer-6330-79' class='  ays_position_initial '>\n                        C) obtuse\n                    <\/label>\n                    <label for='ays-answer-6330-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1634]' id='ays-answer-6327-79' value='6327'\/>\n\n                    <label for='ays-answer-6327-79' class='  ays_position_initial '>\n                        D) 45\u00b0, 45\u00b0, 60\u00b0\n                    <\/label>\n                    <label for='ays-answer-6327-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1633'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>7 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>7. <strong>The measure of angle \u03b8 between two vectors is always.<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1633]' id='ays-answer-6325-79' value='6325'\/>\n\n                    <label for='ays-answer-6325-79' class='  ays_position_initial '>\n                        A) 0 \u2264 \u03b8 \u2264 \u03c0\n                    <\/label>\n                    <label for='ays-answer-6325-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1633]' id='ays-answer-6323-79' value='6323'\/>\n\n                    <label for='ays-answer-6323-79' class='  ays_position_initial '>\n                        B) 0 < \u03b8 < \u03c0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-6323-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1633]' id='ays-answer-6324-79' value='6324'\/>\n\n                    <label for='ays-answer-6324-79' class='  ays_position_initial '>\n                        C) 0 \u2264 \u03b8 \u2264 \u03c0\/2\n                    <\/label>\n                    <label for='ays-answer-6324-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1633]' id='ays-answer-6326-79' value='6326'\/>\n\n                    <label for='ays-answer-6326-79' class='  ays_position_initial '>\n                        D) obtuse\n                    <\/label>\n                    <label for='ays-answer-6326-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1624'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>8 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>8. <strong>The vector whose magnitude is 1 is called<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1624]' id='ays-answer-6289-79' value='6289'\/>\n\n                    <label for='ays-answer-6289-79' class='  ays_position_initial '>\n                        A) free vector\n                    <\/label>\n                    <label for='ays-answer-6289-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1624]' id='ays-answer-6288-79' value='6288'\/>\n\n                    <label for='ays-answer-6288-79' class='  ays_position_initial '>\n                        B) unit vector\n                    <\/label>\n                    <label for='ays-answer-6288-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1624]' id='ays-answer-6287-79' value='6287'\/>\n\n                    <label for='ays-answer-6287-79' class='  ays_position_initial '>\n                        C) Null vector\n                    <\/label>\n                    <label for='ays-answer-6287-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1624]' id='ays-answer-6290-79' value='6290'\/>\n\n                    <label for='ays-answer-6290-79' class='  ays_position_initial '>\n                        D) scalar\n                    <\/label>\n                    <label for='ays-answer-6290-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1632'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>9 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">9. <b>If the dot product of two vectors is zero, then the vectors must be<\/b><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1632]' id='ays-answer-6319-79' value='6319'\/>\n\n                    <label for='ays-answer-6319-79' class='  ays_position_initial '>\n                        A) Parallel\n                    <\/label>\n                    <label for='ays-answer-6319-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1632]' id='ays-answer-6320-79' value='6320'\/>\n\n                    <label for='ays-answer-6320-79' class='  ays_position_initial '>\n                        B) orthogonal\n                    <\/label>\n                    <label for='ays-answer-6320-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1632]' id='ays-answer-6321-79' value='6321'\/>\n\n                    <label for='ays-answer-6321-79' class='  ays_position_initial '>\n                        C) reciprocal\n                    <\/label>\n                    <label for='ays-answer-6321-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1632]' id='ays-answer-6322-79' value='6322'\/>\n\n                    <label for='ays-answer-6322-79' class='  ays_position_initial '>\n                        D) equal\n                    <\/label>\n                    <label for='ays-answer-6322-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1626'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>10 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>10. <strong>Two vectors are said to be negative of each other if they have the same magnitude and __________direction.<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1626]' id='ays-answer-6296-79' value='6296'\/>\n\n                    <label for='ays-answer-6296-79' class='  ays_position_initial '>\n                        A) opposite\n                    <\/label>\n                    <label for='ays-answer-6296-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1626]' id='ays-answer-6297-79' value='6297'\/>\n\n                    <label for='ays-answer-6297-79' class='  ays_position_initial '>\n                        B) negative\n                    <\/label>\n                    <label for='ays-answer-6297-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1626]' id='ays-answer-6295-79' value='6295'\/>\n\n                    <label for='ays-answer-6295-79' class='  ays_position_initial '>\n                        C) Same\n                    <\/label>\n                    <label for='ays-answer-6295-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1626]' id='ays-answer-6298-79' value='6298'\/>\n\n                    <label for='ays-answer-6298-79' class='  ays_position_initial '>\n                        D) parallel\n                    <\/label>\n                    <label for='ays-answer-6298-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1637'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>11 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>11. <strong>The angles \u03b1, \u03b2, and \u03b3 which a non-zero vector r makes with x-axis, y-axis and z \u2212 axis respectively are called_____________ of r.<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1637]' id='ays-answer-6342-79' value='6342'\/>\n\n                    <label for='ays-answer-6342-79' class='  ays_position_initial '>\n                        A) inclinations\n                    <\/label>\n                    <label for='ays-answer-6342-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1637]' id='ays-answer-6339-79' value='6339'\/>\n\n                    <label for='ays-answer-6339-79' class='  ays_position_initial '>\n                        B) Direction cosines\n                    <\/label>\n                    <label for='ays-answer-6339-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1637]' id='ays-answer-6340-79' value='6340'\/>\n\n                    <label for='ays-answer-6340-79' class='  ays_position_initial '>\n                        C) direction ratios\n                    <\/label>\n                    <label for='ays-answer-6340-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1637]' id='ays-answer-6341-79' value='6341'\/>\n\n                    <label for='ays-answer-6341-79' class='  ays_position_initial '>\n                        D) direction angles\n                    <\/label>\n                    <label for='ays-answer-6341-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1629'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>12 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>12. <strong>If \u03b8 be the angle between two vectors a and b, then the projection of b along a is<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1629]' id='ays-answer-6307-79' value='6307'\/>\n\n                    <label for='ays-answer-6307-79' class='  ays_position_initial '>\n                        A) a\u00d7b\/|a||b|\n                    <\/label>\n                    <label for='ays-answer-6307-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1629]' id='ays-answer-6310-79' value='6310'\/>\n\n                    <label for='ays-answer-6310-79' class='  ays_position_initial '>\n                        B) a.b\/|b|\n                    <\/label>\n                    <label for='ays-answer-6310-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1629]' id='ays-answer-6309-79' value='6309'\/>\n\n                    <label for='ays-answer-6309-79' class='  ays_position_initial '>\n                        C) a.b\/|a|\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-6309-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1629]' id='ays-answer-6308-79' value='6308'\/>\n\n                    <label for='ays-answer-6308-79' class='  ays_position_initial '>\n                        D) a.b\/|a||b|\n                    <\/label>\n                    <label for='ays-answer-6308-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1631'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>13 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>13. <strong>If the cross product of two vectors is zero, then the vectors must be<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1631]' id='ays-answer-6318-79' value='6318'\/>\n\n                    <label for='ays-answer-6318-79' class='  ays_position_initial '>\n                        A) Non coplanar\n                    <\/label>\n                    <label for='ays-answer-6318-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1631]' id='ays-answer-6315-79' value='6315'\/>\n\n                    <label for='ays-answer-6315-79' class='  ays_position_initial '>\n                        B) Parallel\n                    <\/label>\n                    <label for='ays-answer-6315-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1631]' id='ays-answer-6317-79' value='6317'\/>\n\n                    <label for='ays-answer-6317-79' class='  ays_position_initial '>\n                        C) reciprocal\n                    <\/label>\n                    <label for='ays-answer-6317-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1631]' id='ays-answer-6316-79' value='6316'\/>\n\n                    <label for='ays-answer-6316-79' class='  ays_position_initial '>\n                        D) orthogonal\n                    <\/label>\n                    <label for='ays-answer-6316-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1643'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>14 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>14. <strong>The lines joining the mid-points of any two sides of a triangle is always _____to the third side.<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1643]' id='ays-answer-6366-79' value='6366'\/>\n\n                    <label for='ays-answer-6366-79' class='  ays_position_initial '>\n                        A) base\n                    <\/label>\n                    <label for='ays-answer-6366-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1643]' id='ays-answer-6363-79' value='6363'\/>\n\n                    <label for='ays-answer-6363-79' class='  ays_position_initial '>\n                        B) Equal\n                    <\/label>\n                    <label for='ays-answer-6363-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1643]' id='ays-answer-6365-79' value='6365'\/>\n\n                    <label for='ays-answer-6365-79' class='  ays_position_initial '>\n                        C) perpendicular\n                    <\/label>\n                    <label for='ays-answer-6365-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1643]' id='ays-answer-6364-79' value='6364'\/>\n\n                    <label for='ays-answer-6364-79' class='  ays_position_initial '>\n                        D) Parallel\n                    <\/label>\n                    <label for='ays-answer-6364-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1625'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>15 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>15. If the terminal point B of the vector <strong>AB<\/strong>\u00a0coincides with its initial point A, then |<strong>AB<\/strong>| = |<strong>BB<\/strong>| =<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1625]' id='ays-answer-6291-79' value='6291'\/>\n\n                    <label for='ays-answer-6291-79' class='  ays_position_initial '>\n                        A) 1\n                    <\/label>\n                    <label for='ays-answer-6291-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1625]' id='ays-answer-6292-79' value='6292'\/>\n\n                    <label for='ays-answer-6292-79' class='  ays_position_initial '>\n                        B) 0\n                    <\/label>\n                    <label for='ays-answer-6292-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1625]' id='ays-answer-6293-79' value='6293'\/>\n\n                    <label for='ays-answer-6293-79' class='  ays_position_initial '>\n                        C) 2\n                    <\/label>\n                    <label for='ays-answer-6293-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1625]' id='ays-answer-6294-79' value='6294'\/>\n\n                    <label for='ays-answer-6294-79' class='  ays_position_initial '>\n                        D) undefined\n                    <\/label>\n                    <label for='ays-answer-6294-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1642'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>16 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>16. <strong>A point P in space has __________ coordinates.<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1642]' id='ays-answer-6359-79' value='6359'\/>\n\n                    <label for='ays-answer-6359-79' class='  ays_position_initial '>\n                        A) 1\n                    <\/label>\n                    <label for='ays-answer-6359-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1642]' id='ays-answer-6361-79' value='6361'\/>\n\n                    <label for='ays-answer-6361-79' class='  ays_position_initial '>\n                        B) 3\n                    <\/label>\n                    <label for='ays-answer-6361-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1642]' id='ays-answer-6360-79' value='6360'\/>\n\n                    <label for='ays-answer-6360-79' class='  ays_position_initial '>\n                        C) 2\n                    <\/label>\n                    <label for='ays-answer-6360-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1642]' id='ays-answer-6362-79' value='6362'\/>\n\n                    <label for='ays-answer-6362-79' class='  ays_position_initial '>\n                        D) infinitely many\n                    <\/label>\n                    <label for='ays-answer-6362-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1628'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>17 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p class=\"MsoNormal\">17. <b>The vector whose initial point is at the origin and terminal point is P, is called<\/b><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1628]' id='ays-answer-6304-79' value='6304'\/>\n\n                    <label for='ays-answer-6304-79' class='  ays_position_initial '>\n                        A) unit vector\n                    <\/label>\n                    <label for='ays-answer-6304-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1628]' id='ays-answer-6305-79' value='6305'\/>\n\n                    <label for='ays-answer-6305-79' class='  ays_position_initial '>\n                        B) position vector\n                    <\/label>\n                    <label for='ays-answer-6305-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1628]' id='ays-answer-6306-79' value='6306'\/>\n\n                    <label for='ays-answer-6306-79' class='  ays_position_initial '>\n                        C) normal vector\n                    <\/label>\n                    <label for='ays-answer-6306-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1628]' id='ays-answer-6303-79' value='6303'\/>\n\n                    <label for='ays-answer-6303-79' class='  ays_position_initial '>\n                        D) Null vector\n                    <\/label>\n                    <label for='ays-answer-6303-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1636'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>18 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>18. <strong>Measures of direction angles \u03b1, \u03b2 and \u03b3 are<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1636]' id='ays-answer-6336-79' value='6336'\/>\n\n                    <label for='ays-answer-6336-79' class='  ays_position_initial '>\n                        A) 0 \u2264 \u03b1 \u2264 \u03c0\/2 , 0 \u2264 \u03b2 \u2264 \u03c0\/2, 0 \u2264 \u03b3 \u2264 \u03c0\/2\n                    <\/label>\n                    <label for='ays-answer-6336-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1636]' id='ays-answer-6338-79' value='6338'\/>\n\n                    <label for='ays-answer-6338-79' class='  ays_position_initial '>\n                        B) 0 \u2264 \u03b1 \u2264 \u03c0, 0 \u2264 \u03b2 \u2264 \u03c0, 0 \u2264 \u03b3 \u2264 \u03c0\n                    <\/label>\n                    <label for='ays-answer-6338-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1636]' id='ays-answer-6335-79' value='6335'\/>\n\n                    <label for='ays-answer-6335-79' class='  ays_position_initial '>\n                        C) \u03b1 \u2264 0, \u03b2 \u2264 0, \u03b3 \u2264 0\n                    <\/label>\n                    <label for='ays-answer-6335-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1636]' id='ays-answer-6337-79' value='6337'\/>\n\n                    <label for='ays-answer-6337-79' class='  ays_position_initial '>\n                        D) \u03b1 \u2265 0, \u03b2 \u2265 0, \u03b3 \u2265 0\n                    <\/label>\n                    <label for='ays-answer-6337-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1638'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>19 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>19. <strong>u = 2i + 3j + k,v = \u22126i \u2212 9j \u2212 3k are _________vectors.<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1638]' id='ays-answer-6344-79' value='6344'\/>\n\n                    <label for='ays-answer-6344-79' class='  ays_position_initial '>\n                        A) perpendicular\n                    <\/label>\n                    <label for='ays-answer-6344-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1638]' id='ays-answer-6345-79' value='6345'\/>\n\n                    <label for='ays-answer-6345-79' class='  ays_position_initial '>\n                        B) reciprocal\n                    <\/label>\n                    <label for='ays-answer-6345-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1638]' id='ays-answer-6346-79' value='6346'\/>\n\n                    <label for='ays-answer-6346-79' class='  ays_position_initial '>\n                        C) negative\n                    <\/label>\n                    <label for='ays-answer-6346-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1638]' id='ays-answer-6343-79' value='6343'\/>\n\n                    <label for='ays-answer-6343-79' class='  ays_position_initial '>\n                        D) Parallel\n                    <\/label>\n                    <label for='ays-answer-6343-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1639'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>20 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>20. <strong>In space the vector k can be written as<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1639]' id='ays-answer-6347-79' value='6347'\/>\n\n                    <label for='ays-answer-6347-79' class='  ays_position_initial '>\n                        A) (1,0,0)\n                    <\/label>\n                    <label for='ays-answer-6347-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1639]' id='ays-answer-6348-79' value='6348'\/>\n\n                    <label for='ays-answer-6348-79' class='  ays_position_initial '>\n                        B) (0,1,0)\n                    <\/label>\n                    <label for='ays-answer-6348-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1639]' id='ays-answer-6350-79' value='6350'\/>\n\n                    <label for='ays-answer-6350-79' class='  ays_position_initial '>\n                        C) (1,0)\n                    <\/label>\n                    <label for='ays-answer-6350-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1639]' id='ays-answer-6349-79' value='6349'\/>\n\n                    <label for='ays-answer-6349-79' class='  ays_position_initial '>\n                        D) (0,0,1)\n                    <\/label>\n                    <label for='ays-answer-6349-79' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                            \n                            <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                            <input type='button' name='next' class='ays_previous action-button '  value='Prev' \/>\n                            <i class='ays_display_none ays_fa ays_fa_arrow_right ays_finish action-button ays_arrow ays_next_arrow'><\/i><input type='button' name='next' class='  ays_next action-button' value='Finish' \/>\n                        <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step'>\n                    <div class='ays-abs-fs ays-end-page information_form'>\n                    <div class='ays-form-title'><\/div>\n                        <input id='ays_form_field_ays_user_name_79' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_name' placeholder='Name' \/><input id='ays_form_field_ays_user_email_79' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_email' placeholder='Email' \/><input id='ays_form_field_ays_user_phone_79' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_phone' placeholder='Phone Number' \/>\n                        <div class='ays_buttons_div'>\n                            <i class='ays_display_none ays_fa ays_fa_flag_checkered ays_finish action-button ays_arrow ays_next_arrow'><\/i>\n                            <input type='submit' name='ays_finish_quiz' class=' ays_next ays_finish action-button' value='See Result'\/>\n                        <\/div>\n                    <\/div>\n                  <\/div><div class='step ays_thank_you_fs'>\n            <div class='ays-abs-fs ays-end-page'>\n            <div style='text-align:center;'><div data-class='lds-ellipsis' data-role='loader' class='ays-loader'><div><\/div><div><\/div><div><\/div><div><\/div><\/div><\/div><div class='ays_quiz_results_page'><div class='ays_score_message'><\/div><div class='ays_message'><\/div><p class='ays_score ays_score_display_none animated'>Your score is <\/p><div class='ays-progress first'>\n                <span class='ays-progress-value first'>0%<\/span>\n                <div class='ays-progress-bg first'>\n                    <div class='ays-progress-bar first' style='width:0%;'><\/div>\n                <\/div>\n            <\/div><p class='ays_restart_button_p'><button type='button' class='action-button ays_restart_button'>\n                    <i class='ays_fa ays_fa_undo'><\/i>\n                    <span>Restart quiz<\/span>\n                <\/button><\/p><\/div><\/div><\/div><style> div#ays-quiz-container-79 * { box-sizing: border-box; } \/* Styles for Internet Explorer start *\/ #ays-quiz-container-79 #ays_finish_quiz_79 { } \/* Styles for Quiz container *\/ #ays-quiz-container-79{ min-height: 350px; width:100%; background-color:#f2f2f2; background-position:center center;border-radius:0px 0px 0px 0px;box-shadow: 0px 0px 15px 1px rgba(0,0,0,0.4);border-width: 1px;border-style: solid;border-color: #2fa0ca;} \/* Styles for Navigation bar *\/ #ays-quiz-questions-nav-wrap-79 { width: 100%;border-radius:0px 0px 0px 0px;box-shadow: 0px 0px 15px 1px rgba(0,0,0,0.4);border-width: 1px;border-style: solid;border-color: #2fa0ca;} #ays-quiz-questions-nav-wrap-79 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question { color: #000000; border-color: #000000; background-color: #f2f2f2; } #ays-quiz-questions-nav-wrap-79 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item.ays-quiz-questions-nav-item-active a.ays_questions_nav_question { box-shadow: inset 0 0 5px #000000, 0 0 5px #000000; } #ays-quiz-questions-nav-wrap-79 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item.ays-quiz-questions-nav-item-answered a.ays_questions_nav_question { color: #f2f2f2; border-color: #f2f2f2; background-color: #000000; } #ays-quiz-questions-nav-wrap-79 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question.ays_quiz_correct_answer { color: rgba(39, 174, 96, 1); border-color: rgba(39, 174, 96, 1); background-color: rgba(39, 174, 96, 0.4); } #ays-quiz-questions-nav-wrap-79 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question.ays_quiz_wrong_answer { color: rgba(243, 134, 129, 1); border-color: rgba(243, 134, 129, 1); background-color: rgba(243, 134, 129, 0.4); } \/* Styles for questions *\/ #ays-quiz-container-79 #ays_finish_quiz_79 div.step { min-height: 350px; } \/* Styles for text inside quiz container *\/ #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays-start-page *:not(input), #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays_question_hint, #ays-quiz-container-79.ays-quiz-container .ays-questions-container label[for^=\"ays-answer-\"], #ays-quiz-container-79.ays-quiz-container .ays-questions-container p, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays-fs-title, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays-fs-subtitle, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .logged_in_message, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays-quiz-limitation-count-of-takers, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays-quiz-limitation-count-of-takers *, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays_score_message, #ays-quiz-container-79.ays-quiz-container .ays-questions-container .ays_message{ color: #000000; outline: none; } \/* Quiz title \/ transformation *\/ #ays-quiz-container-79 .ays-fs-title{ text-transform: uppercase; text-align: center; text-shadow: none; } #ays-quiz-container-79 .ays-quiz-password-message-box, #ays-quiz-container-79 .ays-quiz-question-note-message-box, #ays-quiz-container-79 .ays_quiz_question, #ays-quiz-container-79 .ays_quiz_question *:not([class^='enlighter']) { color: #000000; } #ays-quiz-container-79 textarea, #ays-quiz-container-79 input::first-letter, #ays-quiz-container-79 select::first-letter, #ays-quiz-container-79 option::first-letter { color: initial !important; } #ays-quiz-container-79 p::first-letter:not(.ays_no_questions_message) { color: #000000 !important; background-color: transparent !important; font-size: inherit !important; font-weight: inherit !important; float: none !important; line-height: inherit !important; margin: 0 !important; padding: 0 !important; } #ays-quiz-container-79 .select2-container, #ays-quiz-container-79 .ays-field * { font-size: 16px !important; } #ays-quiz-container-79 .ays-fs-subtitle p { text-align: center ; } #ays-quiz-container-79 .ays_quiz_question p { font-size: 17px; text-align: center; } #ays-quiz-container-79 .ays_quiz_question { text-align: center ; margin-bottom: 10px; } #ays-quiz-container-79 .ays_quiz_question pre { max-width: 100%; white-space: break-spaces; } div#ays-quiz-container-79 .ays-questions-container .ays-field, div#ays-quiz-container-79 .ays-questions-container .ays-field input~label[for^='ays-answer-'], div#ays-quiz-container-79 .ays-questions-container .ays-modern-dark-question *, div#ays-quiz-container-79 .ays-questions-container .ays_quiz_question, div#ays-quiz-container-79 .ays-questions-container .ays_quiz_question *{ word-break: break-word; } #ays-quiz-container-79 .ays-quiz-timer p { font-size: 16px; } #ays-quiz-container-79 section.ays_quiz_redirection_timer_container hr, #ays-quiz-container-79 section.ays_quiz_timer_container hr { margin: 0; } #ays-quiz-container-79 section.ays_quiz_timer_container.ays_quiz_timer_red_warning .ays-quiz-timer { color: red; } #ays-quiz-container-79 .ays_thank_you_fs p { text-align: center; } #ays-quiz-container-79 .information_form input[type='text'], #ays-quiz-container-79 .information_form input[type='url'], #ays-quiz-container-79 .information_form input[type='number'], #ays-quiz-container-79 .information_form input[type='email'], #ays-quiz-container-79 .information_form input[type='tel'], #ays-quiz-container-79 .information_form textarea, #ays-quiz-container-79 .information_form select, #ays-quiz-container-79 .information_form option { color: initial !important; outline: none; margin-left: 0; background-image: unset; } #ays-quiz-container-79 .information_form input[type='checkbox'] { margin: 0 10px; outline: initial; -webkit-appearance: auto; -moz-appearance: auto; position: initial; width: initial; height: initial; border: initial; background: initial; } #ays-quiz-container-79 .information_form input[type='checkbox']::after { content: none; } #ays-quiz-container-79 .wrong_answer_text{ color:#ff4d4d; } #ays-quiz-container-79 .right_answer_text{ color:#33cc33; } #ays-quiz-container-79 .ays_cb_and_a, #ays-quiz-container-79 .ays_cb_and_a * { color: rgb(0,0,0); text-align: center; } #ays-quiz-container-79 iframe { \/*min-height: 350px;*\/ } #ays-quiz-container-79 label.ays_for_checkbox, #ays-quiz-container-79 span.ays_checkbox_for_span { color: initial !important; display: block; } \/* Quiz textarea height *\/ #ays-quiz-container-79 textarea { height: 100px; min-height: 100px; } \/* Quiz rate and passed users count *\/ #ays-quiz-container-79 .ays_quizn_ancnoxneri_qanak, #ays-quiz-container-79 .ays_quiz_rete_avg{ color:#f2f2f2; background-color:#000000; } #ays-quiz-container-79 .ays-questions-container > .ays_quizn_ancnoxneri_qanak { padding: 5px 20px; } #ays-quiz-container-79 div.for_quiz_rate.ui.star.rating .icon { color: rgba(0,0,0,0.35); } #ays-quiz-container-79 .ays_quiz_rete_avg div.for_quiz_rate_avg.ui.star.rating .icon { color: rgba(242,242,242,0.5); } #ays-quiz-container-79 .ays_quiz_rete .ays-quiz-rate-link-box .ays-quiz-rate-link { color: #000000; } \/* Loaders *\/ #ays-quiz-container-79 div.lds-spinner, #ays-quiz-container-79 div.lds-spinner2 { color: #000000; } #ays-quiz-container-79 div.lds-spinner div:after, #ays-quiz-container-79 div.lds-spinner2 div:after { background-color: #000000; } #ays-quiz-container-79 .lds-circle, #ays-quiz-container-79 .lds-facebook div, #ays-quiz-container-79 .lds-ellipsis div{ background: #000000; } #ays-quiz-container-79 .lds-ripple div{ border-color: #000000; } #ays-quiz-container-79 .lds-dual-ring::after, #ays-quiz-container-79 .lds-hourglass::after{ border-color: #000000 transparent #000000 transparent; } \/* Stars *\/ #ays-quiz-container-79 .ui.rating .icon, #ays-quiz-container-79 .ui.rating .icon:before { font-family: Rating !important; } \/* Progress bars *\/ #ays-quiz-container-79 #ays_finish_quiz_79 .ays-progress { border-color: rgba(0,0,0,0.8); } #ays-quiz-container-79 #ays_finish_quiz_79 .ays-progress-bg { background-color: rgba(0,0,0,0.3); } #ays-quiz-container-79 . { background-color: #2fa0ca; } #ays-quiz-container-79 . { background-color: #000000; } #ays-quiz-container-79 .ays-progress-value { color: #000000; text-align: center; } #ays-quiz-container-79 .ays-progress-bar { background-color: #2fa0ca; } #ays-quiz-container-79 .ays-question-counter .ays-live-bar-wrap { direction:ltr !important; } #ays-quiz-container-79 .ays-live-bar-fill{ color: #000000; border-bottom: 2px solid rgba(0,0,0,0.8); text-shadow: 0px 0px 5px #f2f2f2; } #ays-quiz-container-79 .ays-live-bar-fill.ays-live-fourth, #ays-quiz-container-79 .ays-live-bar-fill.ays-live-third, #ays-quiz-container-79 .ays-live-bar-fill.ays-live-second { text-shadow: unset; } #ays-quiz-container-79 .ays-live-bar-percent{ display:none; } \/* Music, Sound *\/ #ays-quiz-container-79 .ays_music_sound { color:rgb(0,0,0); } \/* Dropdown questions scroll bar *\/ #ays-quiz-container-79 blockquote { border-left-color: #000000 !important; } \/* Question hint *\/ #ays-quiz-container-79 .ays_question_hint_container .ays_question_hint_text { background-color:#f2f2f2; box-shadow: 0 0 15px 3px rgba(0,0,0,0.6); max-width: 270px; } #ays-quiz-container-79 .ays_question_hint_container .ays_question_hint_text p { max-width: unset; } #ays-quiz-container-79 .ays_questions_hint_max_width_class { 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This is the last chapter of 2nd-year Maths and is the most important one. There&hellip;<\/p>\n","protected":false},"author":2,"featured_media":263,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[8,9],"class_list":["post-262","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math","tag-ecat-mcqs","tag-entry-test-preparation","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>2nd Year Math Chapter 7 Vectors MCQs With Answers<\/title>\n<meta name=\"description\" content=\"Students can get the 2nd Year Math Chapter 7 Vectors MCQs With Answers here online. 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