{"id":6902,"date":"2021-10-21T22:21:44","date_gmt":"2021-10-21T16:51:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6902"},"modified":"2021-10-25T10:07:52","modified_gmt":"2021-10-25T04:37:52","slug":"find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/","title":{"rendered":"Find the vector of magnitude 5 which are perpendicular to the vectors \\(\\vec{a}\\) = \\(2\\hat{i} + \\hat{j} – 3\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} – 2\\hat{j} + \\hat{k}\\)"},"content":{"rendered":"

Solution :<\/h2>\n

Unit vectors perpendicular to \\(\\vec{a}\\) & \\(\\vec{b}\\) = \\(\\pm\\)\\(\\vec{a}\\times\\vec{b}\\over |\\vec{a}\\times\\vec{b}|\\)<\/p>\n

\\(\\therefore\\)\u00a0 \\(\\vec{a}\\times\\vec{b}\\) = \\(\\begin{vmatrix}
\n\\hat{i} & \\hat{j} & \\hat{k} \\\\
\n2 & 1 & -3 \\\\
\n1 & 2 & -2 \\\\
\n\\end{vmatrix}\\) = \\(-5\\hat{i} – 5\\hat{j} – 5\\hat{k}\\)<\/p>\n

\\(\\therefore\\) Unit Vectors = \\(\\pm\\) \\(-5\\hat{i} – 5\\hat{j} – 5\\hat{k}\\over 5\\sqrt{3}\\)<\/p>\n

Hence the required vectors are \\(\\pm\\) \\(5\\sqrt{3}\\over 3\\)(\\(\\hat{i} + \\hat{j} + \\hat{k}\\))<\/p>\n

\n

Similar Questions<\/h3>\n

Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.<\/a><\/p>\n

Find dot product of vectors \\(\\vec{a}\\) = \\(2\\hat{i}+2\\hat{j}-\\hat{k}\\) and \\(\\vec{b}\\) = \\(6\\hat{i}-3\\hat{j}+2\\hat{k}\\)<\/a><\/p>\n

For any three vectors \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\) prove that [\\(\\vec{a}\\) + \\(\\vec{b}\\) \\(\\vec{b}\\) + \\(\\vec{c}\\) \\(\\vec{c}\\) + \\(\\vec{a}\\)] = 2[\\(\\vec{a}\\) \\(\\vec{b}\\) \\(\\vec{c}\\)]<\/a><\/p>\n

If \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\) are three non zero vectors such that \\(\\vec{a}\\times\\vec{b}\\) = \\(\\vec{c}\\) and \\(\\vec{b}\\times\\vec{c}\\) = \\(\\vec{a}\\), prove that \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\) are mutually at right angles and |\\(\\vec{b}\\)| = 1 and |\\(\\vec{c}\\)| = |\\(\\vec{a}\\)|<\/a><\/p>\n

Find the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Unit vectors perpendicular to \\(\\vec{a}\\) & \\(\\vec{b}\\) = \\(\\pm\\)\\(\\vec{a}\\times\\vec{b}\\over |\\vec{a}\\times\\vec{b}|\\) \\(\\therefore\\)\u00a0 \\(\\vec{a}\\times\\vec{b}\\) = \\(\\begin{vmatrix} \\hat{i} & \\hat{j} & \\hat{k} \\\\ 2 & 1 & -3 \\\\ 1 & 2 & -2 \\\\ \\end{vmatrix}\\) = \\(-5\\hat{i} – 5\\hat{j} – 5\\hat{k}\\) \\(\\therefore\\) Unit Vectors = \\(\\pm\\) \\(-5\\hat{i} – 5\\hat{j} – 5\\hat{k}\\over 5\\sqrt{3}\\) Hence the required …<\/p>\n

Find the vector of magnitude 5 which are perpendicular to the vectors \\(\\vec{a}\\) = \\(2\\hat{i} + \\hat{j} – 3\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} – 2\\hat{j} + \\hat{k}\\)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,61],"tags":[],"yoast_head":"\nFind the vector of magnitude 5 which are perpendicular to the vectors \\(\\vec{a}\\) = \\(2\\hat{i} + \\hat{j} - 3\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} - 2\\hat{j} + \\hat{k}\\) - Mathemerize<\/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:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the vector of magnitude 5 which are perpendicular to the vectors \\(\\vec{a}\\) = \\(2\\hat{i} + \\hat{j} - 3\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} - 2\\hat{j} + \\hat{k}\\) - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Unit vectors perpendicular to (vec{a}) & (vec{b}) = (pm)(vec{a}timesvec{b}over |vec{a}timesvec{b}|) (therefore)\u00a0 (vec{a}timesvec{b}) = (begin{vmatrix} hat{i} & hat{j} & hat{k} \\ 2 & 1 & -3 \\ 1 & 2 & -2 \\ end{vmatrix}) = (-5hat{i} – 5hat{j} – 5hat{k}) (therefore) Unit Vectors = (pm) (-5hat{i} – 5hat{j} – 5hat{k}over 5sqrt{3}) Hence the required … Find the vector of magnitude 5 which are perpendicular to the vectors (vec{a}) = (2hat{i} + hat{j} – 3hat{k}) and (vec{b}) = (hat{i} – 2hat{j} + hat{k}) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T16:51:44+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:37:52+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Find the vector of magnitude 5 which are perpendicular to the vectors \\\\(\\\\vec{a}\\\\) = \\\\(2\\\\hat{i} + \\\\hat{j} – 3\\\\hat{k}\\\\) and \\\\(\\\\vec{b}\\\\) = \\\\(\\\\hat{i} – 2\\\\hat{j} + \\\\hat{k}\\\\)\",\"datePublished\":\"2021-10-21T16:51:44+00:00\",\"dateModified\":\"2021-10-25T04:37:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/\"},\"wordCount\":251,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Vectors Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/\",\"url\":\"https:\/\/mathemerize.com\/find-the-vector-of-magnitude-5-which-are-perpendicular-to-the-vectors-veca-2hati-hatj-3hatk-and-vecb-hati-2hatj-hatk\/\",\"name\":\"Find the vector of magnitude 5 which are perpendicular to the vectors \\\\(\\\\vec{a}\\\\) = \\\\(2\\\\hat{i} + \\\\hat{j} - 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