{"id":14812,"date":"2021-05-12T17:01:27","date_gmt":"2021-05-12T11:31:27","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=14812"},"modified":"2022-04-08T19:58:00","modified_gmt":"2022-04-08T14:28:00","slug":"2-1-n-vector-introduction-exercise-problems","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=14812","title":{"rendered":"2.1 &#8211; N &#8211; Vector Introduction &#8211; Exercise Problems"},"content":{"rendered":"\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ A}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\  If\\ \\overrightarrow{a}= 3\\overrightarrow{i}\\ + 2\\overrightarrow{j} + \\overrightarrow{k}\\ and\\  \\overrightarrow{b}= \\overrightarrow{i}\\ + 3\\overrightarrow{j} + \\overrightarrow{k}\\, find\\   3\\overrightarrow{a}\\ +\\   \\overrightarrow{b}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\  If\\ \\overrightarrow{a}= 2\\overrightarrow{i}\\ + 3\\overrightarrow{j} + \\overrightarrow{k}\\ and\\  \\overrightarrow{b}= 3\\overrightarrow{i}\\ &#8211; \\overrightarrow{j} + \\overrightarrow{k}\\, find\\   2\\overrightarrow{a}\\ +\\   3\\overrightarrow{b}\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ If\\ position\\ vectors\\ of\\ the\\ points\\ A\\ and\\ B\\ are\\  2\\overrightarrow{i}\\ -\\overrightarrow{j} +  3\\overrightarrow{k}\\ and\\ 5\\overrightarrow{i}\\ + \\overrightarrow{j} &#8211; 2\\overrightarrow{k}\\ find\\  \\overrightarrow{|AB|}\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ Find\\ the\\ unit\\ vector\\ along\\ the\\ vector\\ 2\\overrightarrow{i}\\ &#8211; \\overrightarrow{j}- \\overrightarrow{k}\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ Find\\ the\\ direction\\ cosines\\ of\\ the\\ vector\\ 3\\overrightarrow{i}\\ +\\ 4 \\overrightarrow{j}-\\ 5 \\overrightarrow{k}\\ \\hspace{20cm}\\]<\/div>\n\n\n\n<div class=\"aicp\"><script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- Ad1 -->\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"8240817448\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ B}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ If\\ the\\ position\\ vector\\ of\\ the\\ points\\ A\\ and\\ B\\ are\\ \\hspace{15cm}\\]\\[\\overrightarrow{i}\\ -\\ \\overrightarrow{j}\\ +\\  \\overrightarrow{k}\\ and\\  3\\overrightarrow{i}\\ +\\  2\\overrightarrow{j}\\ +\\ 3\\overrightarrow{k},\\ \\hspace{12cm}\\]\\[find\\ \\overrightarrow{|AB|}\\ ,\\ Also\\ find\\ the\\ direction\\ ratio\\ of\\ \\overrightarrow{AB}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ Find\\ the\\  Modulus\\ and\\ Direction\\  cosines\\ \\hspace{15cm}\\]\\[of\\ the\\ vector\\  2\\overrightarrow{i}\\ + 3\\overrightarrow{j}\\ +\\ 4\\overrightarrow{k}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<p>7.  Show that the points whose position vectors  <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2\\overrightarrow{i}\\ &#8211; \\overrightarrow{j} + 3\\overrightarrow{k},\\  3\\overrightarrow{i}\\ &#8211; 5\\overrightarrow{j} + \\overrightarrow{k}\\ and\\ -\\overrightarrow{i}\\ +11 \\overrightarrow{j}+ 9\\overrightarrow{k}\\ are\\ collinear\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"aicp\"><script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\" style=\"display:block; text-align:center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"2812384453\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ C}\\]<\/div>\n\n\n\n<p>8. <span style=\"font-size: revert; color: initial;\">Prove that the points <\/span> <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2\\overrightarrow{i}\\ + 3\\overrightarrow{j}+ 4\\overrightarrow{k},  3\\overrightarrow{i}\\ + 4\\overrightarrow{j}+ 2\\overrightarrow{k} and\\ 4\\overrightarrow{i}\\ +2 \\overrightarrow{j}+ 3\\overrightarrow{k}\\  form\\  an\\ equilateral\\  triangle\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[9.\\ Prove\\ that\\ the\\ points\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3\\overrightarrow{i}\\ -\\ \\overrightarrow{j}\\  -\\ 2 \\overrightarrow{k}\\ ,\\  5\\overrightarrow{i}\\ +\\  \\overrightarrow{j}\\ -\\  3\\overrightarrow{k} and\\ 6\\overrightarrow{i}\\  -\\  \\overrightarrow{j}\\  -\\  \\overrightarrow{k}\\  form\\  an\\ isosceles\\ triangle\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[10.\\ The\\ position\\ vectors\\ of\\ the\\ \\triangle\\ ABC\\ are\\ \\hspace{18cm}\\]\\[2\\overrightarrow{i}\\ &#8211; \\overrightarrow{j}+ \\overrightarrow{k},  \\overrightarrow{i}\\ &#8211; 3\\overrightarrow{j} &#8211; 5\\overrightarrow{k} and\\ 3\\overrightarrow{i}\\ -4 \\overrightarrow{j} &#8211; 4\\overrightarrow{k}\\ respectively.\\ Prove\\ that\\ triangle\\ is\\ right\\ angled\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"aicp\"><script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-format=\"autorelaxed\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"3040040190\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>7. Show that the points whose position vectors 8. Prove that the points<\/p>\n","protected":false},"author":187055548,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[711787920,1],"tags":[],"class_list":["post-14812","post","type-post","status-publish","format-standard","hentry","category-2-1-n-vector-introduction-exercise-problems","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>2.1 - N - Vector Introduction - Exercise Problems - YANAMTAKSHASHILA<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/yanamtakshashila.com\/?p=14812\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2.1 - N - Vector Introduction - Exercise Problems - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"7. 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