{"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":"

Solution :<\/h2>\n

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

\\(\\vec{a}\\).\\(\\vec{b}\\) = (\\(2\\hat{i}+2\\hat{j}-\\hat{k}\\)).(\\(6\\hat{i}-3\\hat{j}+2\\hat{k}\\))<\/p>\n

= (2)(6) + (2)(-3) + (-1)(2) = 12 – 6 – 2 = 4<\/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 the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)<\/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 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":"

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 – 6 – 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 …<\/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}\\)<\/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 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 – 6 – 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 … Find dot product of vectors (vec{a}) = (2hat{i}+2hat{j}-hat{k}) and (vec{b}) = (6hat{i}-3hat{j}+2hat{k}) Read More »\" \/>\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 - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"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}\\)","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/find-dot-product-of-vectors-veca-2hati2hatj-hatk-and-vecb-6hati-3hatj2hatk\/","og_locale":"en_US","og_type":"article","og_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}\\)","og_description":"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 – 6 – 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 … Find dot product of vectors (vec{a}) = (2hat{i}+2hat{j}-hat{k}) and (vec{b}) = (6hat{i}-3hat{j}+2hat{k}) Read More »","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 - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7216"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=7216"}],"version-history":[{"count":2,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7216\/revisions"}],"predecessor-version":[{"id":7544,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7216\/revisions\/7544"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=7216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=7216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=7216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}