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>\nNCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3<\/h2>\n <\/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 <\/p>\nExercise 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 \n\u2234 The given points are collinear.<\/p>\n <\/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
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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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n