{"id":4756,"date":"2023-12-23T09:25:58","date_gmt":"2023-12-23T03:55:58","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=4756"},"modified":"2023-12-23T17:34:59","modified_gmt":"2023-12-23T12:04:59","slug":"samacheer-kalvi-12th-maths-solutions-chapter-6-ex-6-2","status":"publish","type":"post","link":"https:\/\/samacheerguru.com\/samacheer-kalvi-12th-maths-solutions-chapter-6-ex-6-2\/","title":{"rendered":"Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.2"},"content":{"rendered":"

You can Download Samacheer Kalvi 12th Maths Book Solutions<\/a> Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.2<\/h2>\n

Question 1.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 2.
\nFind the volume of the parallelepiped whose coterminous edges are represented by the vectors \"Samacheer.
\nSolution:
\nVolume of the parallelepiped = \\(\\| \\vec{a}, \\vec{b}, \\vec{c}]\\)
\n\"Samacheer
\n= -264 + 224 + 760 = 720 cubic units<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nThe volume of the parallelepiped whose coterminus edges are \"Samacheer, \\(-3 \\vec{i}+7 \\vec{j}+5 \\vec{k}\\) is 90 cubic units. Find the value of \u03bb
\nSolution:
\nGiven, Volume of the parallelepiped = 90 cubic units
\n\"Samacheer<\/p>\n

Question 4.
\nIf \\(\\vec{a}, \\vec{b}, \\vec{c}\\) are three non-coplanar vectors represented by concurrent edges of a parallelepiped of volume 4 cubic units, find the value of \"Samacheer
\nSolution:
\nLet \\(\\vec{a}, \\vec{b}, \\vec{c}\\) be the concurrent edges of parallelepiped
\nGiven volume of parallelepiped = 4 cubic units
\n\"Samacheer<\/p>\n

Question 5.
\nFind the altitude of a parallelepiped determined by the vectors \\(\\vec{a}=-2 \\hat{i}+5 \\hat{j}+3 \\hat{k}\\), \\(\\hat{b}=\\hat{i}+3 \\hat{j}-2 \\hat{k}\\) and \\(\\vec{c}=-3 \\vec{i}+\\vec{j}+4 \\vec{k}\\) if the base is taken as the parallelogram determined by b and c.
\nSolution:
\nVolume = Base Area \u00d7 Height
\n\\(|[\\vec{a}, \\vec{b}, \\vec{c}]|=|\\vec{b} \\times \\vec{c}|\\) \u00d7 Height
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nDetermine whether the three vectors \\(2 \\hat{i}+3 \\hat{j}+\\hat{k}, \\hat{i}-2 \\hat{j}+2 \\hat{k}\\) and \\(3 \\hat{i}+\\hat{j}+3 \\hat{k}\\) are coplanar.
\nSolution:
\n\"Samacheer<\/p>\n

Question 7.
\nLet \"Samacheer If c1<\/sub> = 1 and c2<\/sub> = 2, find c3<\/sub> such that \\(\\vec{a}, \\vec{b}\\) and \\(\\vec{c}\\) and c are coplanar.
\nSolution:
\n\"Samacheer<\/p>\n

Question 8.
\nIf \"Samacheer, show that \\([\\vec{a} \\vec{b} \\vec{c}]\\) depends neither x nor y.
\nSolution:
\n\"Samacheer<\/p>\n

Question 9.
\nIf the vectors
\n\"Samacheer
\nare coplanar, prove that c is the geometric mean of a and b.
\nSolution:
\n\"Samacheer
\n\u2234 c is the geometric means of \u2018a\u2019 and \u2018b’.<\/p>\n

Question 10.
\nLet \\(\\vec{a}, \\vec{b}, \\vec{c}\\) be three non-zero vectors such that \\(\\vec{c}\\) is a unit vector perpendicular to both \\(\\vec{a}\\) and \\(\\vec{b}\\). If the angle between \\(\\vec{a}\\) and \\(\\vec{b}\\) is \\(\\frac{\\pi}{6}\\) show that \"Samacheer .
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.2 Additional Problems<\/h3>\n

Question 1.
\nIf the edges \"Samacheer meet a vertex, find the volume of the parallelepiped.
\nSolution:
\nVolume of the parallelepiped = \"Samacheer
\nThe volume cannot be negative
\n\u2234 Volume of parallelepiped = 264 cu. units<\/p>\n

Question 2.
\nIf \"Samacheer and \\(\\vec{x} \\neq \\overrightarrow{0}\\) then show that \\(\\vec{a}, \\vec{b}, \\vec{c}\\) are coplanar.
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nThe volume of a parallelepiped whose edges are represented by \\(-12 \\vec{i}+\\lambda k\\), \\(3 \\vec{j}-\\vec{k}, 2 \\vec{i}+\\vec{j}-15 \\vec{k}\\) is 546. Find the value of \u03bb.
\nSolution:
\nVolume of the parallelepiped = \"Samacheer
\n= -12 [-45 + 1] – 0 () + \u03bb [0 – 6] = -12 (-44) -6 \u03bb
\n= 528 – 6\u03bb = 546 (given)
\n\u21d2 -6\u03bb = 546 – 528 = 18
\n\u2234 \u03bb = \\(\\frac{18}{-6}\\) = -3<\/p>\n

Question 4.
\nProve that \\(|\\vec{a} \\vec{b} \\vec{c}|\\) = abc if and only if \\(\\vec{a}, \\vec{b}, \\vec{c}\\) are mutually perpendicular.
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 5.
\nShow that the points (1, 3, 1), (1, 1, -1), (-1, 1, 1), (2, 2, -1) are lying on the same plane.
\nSolution:
\n\"Samacheer<\/p>\n

Question 6.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 12th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.2 Question 1. Solution: Question 2. Find the volume of the parallelepiped whose coterminous […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[8],"tags":[],"blocksy_meta":"","jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/4756"}],"collection":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/comments?post=4756"}],"version-history":[{"count":1,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/4756\/revisions"}],"predecessor-version":[{"id":55327,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/4756\/revisions\/55327"}],"wp:attachment":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/media?parent=4756"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/categories?post=4756"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/tags?post=4756"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}