{"id":29718,"date":"2022-03-29T11:00:13","date_gmt":"2022-03-29T05:30:13","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=29718"},"modified":"2022-03-29T11:12:56","modified_gmt":"2022-03-29T05:42:56","slug":"ncert-solutions-for-class-12-maths-chapter-4-ex-4-3","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-3\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 4 Determinants Ex 4.3 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-3\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3<\/h2>\n

\"NCERT<\/p>\n

Ex 4.3 Class 12 NCERT Solutions Question 1.<\/strong>
\nFind the area of the triangle with vertices at the point given in each of the following:
\n(i) (1, 0), (6, 0) (4, 3)
\n(ii) (2, 7), (1, 1), (10, 8)
\n(iii) (- 2, – 3), (3, 2), (- 1, – 8)
\nSolution:
\n\"4.3<\/p>\n

Exercise 4.3 Class 12 NCERT Solutions Question 2.<\/strong>
\nShow that the points A (a, b + c), B (b, c + a) C (c, a+b) are collinear.
\nSolution:
\n\"Ex4.3
\n\u2234 The given points are collinear.<\/p>\n

\"NCERT<\/p>\n

4.3 Class 12 NCERT Solutions Question 3.<\/strong>
\nFind the value of k if area of triangle is 4 square units and vertices are
\n(i) (k, 0), (4, 0), (0, 2)
\n(ii) (-2, 0), (0, 4), (0, k).
\nSolution:
\n(i) Area of \u2206 = 4 (Given)
\n\\(\\frac { 1 }{ 2 } \\left| \\begin{matrix} k\\quad & 0 & \\quad 1 \\\\ 4\\quad & 0 & \\quad 1 \\\\ 0\\quad & 2 & \\quad 1 \\end{matrix} \\right| \\)
\n= \\(\\\\ \\frac { 1 }{ 2 } \\) [-2k+8]
\n= -k+4
\nCase (a): -k + 4 = 4 \u21d2 k = 0
\nCase (b): -k + 4 = -4 \u21d2 k = 8
\nHence, k = 0, 8<\/p>\n

(ii) The area of the triangle whose vertices are (-2,0), (0,4), (0, k)
\n\\(\\frac{1}{2}\\left|\\begin{array}{ccc} -2 & 0 & 1 \\\\ 0 & 4 & 1 \\\\ 0 & k & 1 \\end{array}\\right|\\) =
\n= \u00b1 4 \u21d2 \\(\\frac{1}{2}\\)[- 2(4 – k) – 0 + (0)] = \u00b1 4
\n\u21d2 8 + 2k = \u00b1 8 \u21d2 2k = 16 or 2k = 0 or k = 8<\/p>\n

Exercise 4.3 Class 12 Maths NCERT Solutions Question 4.<\/strong>
\n(i) Find the equation of line joining (1, 2) and (3,6) using determinants.
\n(ii) Find the equation of line joining (3,1), (9,3) using determinants.
\nSolution:
\n(i) Let (x, y) be a point on the line, then the points (x, y), (1, 2) and (3, 6) are collinear.
\n\u2234 \\(\\left|\\begin{array}{lll}
\nx & y & 1 \\\\
\n1 & 2 & 1 \\\\
\n3 & 6 & 1
\n\\end{array}\\right|\\) = 0
\n\u21d2 x(2 – 6) – y(1 – 3) + 1(6 – 6) = 0
\n\u21d2 – 4x + 2y = 0 \u21d2 2x – y = 0
\n\u21d2 y = 2x<\/p>\n

(ii) Let (x, y) be a point on the line. Then (r, y), (3, 1) and (9, 3) are collinear.
\n\u2234 \\(\\left|\\begin{array}{lll}
\nx & y & 1 \\\\
\n3 & 1 & 1 \\\\
\n9 & 3 & 1
\n\\end{array}\\right|\\) = 0
\n\u21d2 x(1 – 3) – y(3 – 9) + 1(9 – 9) = 0
\n\u21d2 2x + 6y = 0 \u21d2 x – 3y = 0<\/p>\n

\"NCERT<\/p>\n

Ex 4.3 Class 12 Maths Ncert Solutions Question 5.<\/strong>
\nIf area of triangle is 35 sq. units with vertices (2, – 6), (5,4) and (k, 4). Then k is
\n(a) 12
\n(b) – 2
\n(c) -12,-2
\n(d) 12,-2
\nSolution:
\n(d) Area of \u2206 = \\(\\frac { 1 }{ 2 } \\left| \\begin{matrix} 2\\quad & -6 & \\quad 1 \\\\ 5\\quad & 4 & \\quad 1 \\\\ k\\quad & 4 & \\quad 1 \\end{matrix} \\right| \\)
\n= \\(\\\\ \\frac { 1 }{ 2 } \\) [50 – 10k] = 25 – 5k
\n\u2234 25 – 5k = 35 or 25 – 5k = – 35
\n– 5k = 10 or 5k = 60
\n\u21d2 k = -2 or k = 12<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-3\/ NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3 Ex 4.3 Class 12 NCERT Solutions Question 1. Find the area of the triangle with vertices at the point given …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 - MCQ Questions<\/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:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-3\/ NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3 Ex 4.3 Class 12 NCERT Solutions Question 1. 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