{"id":7220,"date":"2021-10-23T02:21:43","date_gmt":"2021-10-22T20:51:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7220"},"modified":"2021-10-25T10:04:17","modified_gmt":"2021-10-25T04:34:17","slug":"find-the-vector-equation-of-a-line-which-passes-through-the-point-a-3-4-7-and-b-1-1-6","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-vector-equation-of-a-line-which-passes-through-the-point-a-3-4-7-and-b-1-1-6\/","title":{"rendered":"Find the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)"},"content":{"rendered":"

Solution :<\/h2>\n

We know that the vector equation of line passing through two points with position vectors \\(\\vec{a}\\) and \\(\\vec{b}\\) is,<\/p>\n

\\(\\vec{r}\\) = \\(\\lambda\\) \\((\\vec{b} – \\vec{a})\\)<\/span><\/p>\n

Here \\(\\vec{a}\\) = \\(3\\hat{i} + 4\\hat{j} – 7\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} – \\hat{j} + 6\\hat{k}\\).<\/p>\n

So, the vector equation of the required line is<\/p>\n

\\(\\vec{r}\\) = (\\(3\\hat{i} + 4\\hat{j} – 7\\hat{k}\\)) + \\(\\lambda\\)\u00a0 (\\(\\hat{i} – \\hat{j} + 6\\hat{k}\\) – \\(3\\hat{i} + 4\\hat{j} – 7\\hat{k}\\))<\/p>\n

or, \\(\\vec{r}\\) = (\\(3\\hat{i} + 4\\hat{j} – 7\\hat{k}\\)) + \\(\\lambda\\) (\\(-2\\hat{i} – 5\\hat{j} + 13\\hat{k}\\))<\/p>\n

where \\(\\lambda\\) is a scalar.<\/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 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 know that the vector equation of line passing through two points with position vectors \\(\\vec{a}\\) and \\(\\vec{b}\\) is, \\(\\vec{r}\\) = \\(\\lambda\\) \\((\\vec{b} – \\vec{a})\\) Here \\(\\vec{a}\\) = \\(3\\hat{i} + 4\\hat{j} – 7\\hat{k}\\) and \\(\\vec{b}\\) = \\(\\hat{i} – \\hat{j} + 6\\hat{k}\\). So, the vector equation of the required line is \\(\\vec{r}\\) = (\\(3\\hat{i} …<\/p>\n

Find the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)<\/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 equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)<\/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-equation-of-a-line-which-passes-through-the-point-a-3-4-7-and-b-1-1-6\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the vector equation of a line which passes through the point A (3, 4, -7) and B (1, -1, 6)\" \/>\n<meta property=\"og:description\" content=\"Solution : We know that the vector equation of line passing through two points with position vectors (vec{a}) and (vec{b}) is, (vec{r}) = (lambda) ((vec{b} – vec{a})) Here (vec{a}) = (3hat{i} + 4hat{j} – 7hat{k}) and (vec{b}) = (hat{i} – hat{j} + 6hat{k}). 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