{"id":7216,"date":"2021-10-23T02:19:16","date_gmt":"2021-10-22T20:49:16","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7216"},"modified":"2021-10-25T10:06:54","modified_gmt":"2021-10-25T04:36:54","slug":"find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/","title":{"rendered":"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}\\)"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We have \\(\\vec{a}\\) = \\(2\\hat{i}+2\\hat{j}-\\hat{k}\\) and \\(\\vec{b}\\) = \\(6\\hat{i}-3\\hat{j}+2\\hat{k}\\)<\/p>\n<p>\\(\\vec{a}\\).\\(\\vec{b}\\) = (\\(2\\hat{i}+2\\hat{j}-\\hat{k}\\)).(\\(6\\hat{i}-3\\hat{j}+2\\hat{k}\\))<\/p>\n<p>= (2)(6) + (2)(-3) + (-1)(2) = 12 &#8211; 6 &#8211; 2 = 4<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-angle-between-the-vectors-with-the-direction-ratios-proportional-to-4-3-5-and-3-4-5\/\" aria-label=\"\u201cFind the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.\u201d (Edit)\">Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-vector-equation-of-a-line-which-passes-through-the-point-a-3-4-7-and-b-1-1-6\/\" aria-label=\"\u201cFind the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)\u201d (Edit)\">Find the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/for-any-three-vectors-veca-vecb-vecc-prove-that-veca-vecb-vecb-vecc-vecc-veca-2veca\/\" aria-label=\"\u201cFor 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}\\)]\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-veca-vecb-vecc-are-three-non-zero-vectors-such-that-vecatimesvecb-vecc-and-vecbtimesvecc-veca-prove-that\/\" aria-label=\"\u201cIf \\(\\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}\\)|\u201d (Edit)\">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<p><a class=\"row-title\" 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\/\" aria-label=\"\u201cFind the vector of magnitude 5 which are perpendicular to the vectors \\(\\vec{a}\\) = \\(2\\hat{i} + \\hat{j} \u2013 3\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} \u2013 2\\hat{j} + \\hat{k}\\)\u201d (Edit)\">Find the vector of magnitude 5 which are perpendicular to the vectors \\(\\vec{a}\\) = \\(2\\hat{i} + \\hat{j} \u2013 3\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} \u2013 2\\hat{j} + \\hat{k}\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We have \\(\\vec{a}\\) = \\(2\\hat{i}+2\\hat{j}-\\hat{k}\\) and \\(\\vec{b}\\) = \\(6\\hat{i}-3\\hat{j}+2\\hat{k}\\) \\(\\vec{a}\\).\\(\\vec{b}\\) = (\\(2\\hat{i}+2\\hat{j}-\\hat{k}\\)).(\\(6\\hat{i}-3\\hat{j}+2\\hat{k}\\)) = (2)(6) + (2)(-3) + (-1)(2) = 12 &#8211; 6 &#8211; 2 = 4 Similar Questions Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5. Find the vector equation of a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\"> <span class=\"screen-reader-text\">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}\\)<\/span> Read More &raquo;<\/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":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>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}\\)<\/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-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"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}\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : We have (vec{a}) = (2hat{i}+2hat{j}-hat{k}) and (vec{b}) = (6hat{i}-3hat{j}+2hat{k}) (vec{a}).(vec{b}) = ((2hat{i}+2hat{j}-hat{k})).((6hat{i}-3hat{j}+2hat{k})) = (2)(6) + (2)(-3) + (-1)(2) = 12 &#8211; 6 &#8211; 2 = 4 Similar Questions Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5. Find the vector equation of a &hellip; Find dot product of vectors (vec{a}) = (2hat{i}+2hat{j}-hat{k}) and (vec{b}) = (6hat{i}-3hat{j}+2hat{k}) Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T20:49:16+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:36:54+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-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"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}\\\\)\",\"datePublished\":\"2021-10-22T20:49:16+00:00\",\"dateModified\":\"2021-10-25T04:36:54+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\"},\"wordCount\":209,\"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-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\",\"url\":\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\",\"name\":\"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}\\\\)\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-22T20:49:16+00:00\",\"dateModified\":\"2021-10-25T04:36:54+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"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}\\\\)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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Find the vector equation of a &hellip; Find dot product of vectors (vec{a}) = (2hat{i}+2hat{j}-hat{k}) and (vec{b}) = (6hat{i}-3hat{j}+2hat{k}) Read More &raquo;","og_url":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T20:49:16+00:00","article_modified_time":"2021-10-25T04:36:54+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"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}\\)","datePublished":"2021-10-22T20:49:16+00:00","dateModified":"2021-10-25T04:36:54+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/"},"wordCount":209,"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-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/","url":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/","name":"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}\\)","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-22T20:49:16+00:00","dateModified":"2021-10-25T04:36:54+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"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}\\)"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - 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