{"id":7218,"date":"2021-10-23T02:20:38","date_gmt":"2021-10-22T20:50:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7218"},"modified":"2021-10-25T10:06:47","modified_gmt":"2021-10-25T04:36:47","slug":"find-the-angle-between-the-vectors-with-the-direction-ratios-proportional-to-4-3-5-and-3-4-5","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-angle-between-the-vectors-with-the-direction-ratios-proportional-to-4-3-5-and-3-4-5\/","title":{"rendered":"Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5."},"content":{"rendered":"

Solution :<\/h2>\n

We have,<\/p>\n

\\(\\vec{a}\\) = \\(4\\hat{i} – 3\\hat{j} + 5\\hat{k}\\) and \\(\\vec{b}\\) = \\(3\\hat{i} + 4\\hat{j} + 5\\hat{k}\\)<\/p>\n

Let \\(\\theta\\) is the angle between the given vectors. Then,<\/p>\n

cos\\(\\theta\\) = \\(\\vec{a}.\\vec{b}\\over |\\vec{a}||\\vec{b}|\\)<\/p>\n

\\(\\implies\\) cos\\(\\theta\\) = \\(12 – 12 + 25\\over \\sqrt{16 + 9 + 25} \\sqrt{16 + 9 + 25}\\) = \\(1\\over 2\\)<\/p>\n

\\(\\implies\\) \\(\\theta\\) = \\(\\pi\\over 3\\)<\/p>\n

\n

Similar Questions<\/h3>\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

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 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}\\) = \\(4\\hat{i} – 3\\hat{j} + 5\\hat{k}\\) and \\(\\vec{b}\\) = \\(3\\hat{i} + 4\\hat{j} + 5\\hat{k}\\) Let \\(\\theta\\) is the angle between the given vectors. Then, cos\\(\\theta\\) = \\(\\vec{a}.\\vec{b}\\over |\\vec{a}||\\vec{b}|\\) \\(\\implies\\) cos\\(\\theta\\) = \\(12 – 12 + 25\\over \\sqrt{16 + 9 + 25} \\sqrt{16 + 9 + 25}\\) = \\(1\\over 2\\) \\(\\implies\\) …<\/p>\n

Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.<\/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 angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.<\/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-angle-between-the-vectors-with-the-direction-ratios-proportional-to-4-3-5-and-3-4-5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, (vec{a}) = (4hat{i} – 3hat{j} + 5hat{k}) and (vec{b}) = (3hat{i} + 4hat{j} + 5hat{k}) Let (theta) is the angle between the given vectors. 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