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Ex 4.3, 2 - Show that points A (a, b+c), B (b, c+a), C (c, a+b) are

Ex 4.3, 2 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.3, 2 - Chapter 4 Class 12 Determinants - Part 3 Ex 4.3, 2 - Chapter 4 Class 12 Determinants - Part 4

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Ex 4.3, 2 (Introduction) Show that points A (a , b + c), B (b,c + a), C (c,a + b) are collinear 3 points collinear Area of triangle = 0 Area of triangle ≠ 0 Ex 4.3, 2 Show that points A (a , b + c), B (b, c + a), C (c,a + b) are collinear Three point are collinear if they lie on some line 𝑖.𝑒. They do not form a triangle ∴ Area of triangle = 0 We know that Area of triangle is given by ∆ = 1/2 |■8(x1&y1&[email protected]&y2&[email protected]&y3&1)| Here, x1 = a, y1 = b + c, x2 = b, y2 = c + a, x3 = c , y3 = a + b Putting values ∆ = 1/2 |■8(a&b+c&[email protected]&c+a&[email protected]&a+b&1)| Applying C1 → C1 + C2 ∆ = 1/2 |■8(a+b+c&b+c&[email protected]+c+a&c+a&[email protected]+a+b&a+b&1)| Taking (a + b + c) common from C1 ∆ = 1/2 (a + b + c) |■8(1&b+c&[email protected]&c+a&[email protected]&a+b&1)| Here, 1st and 3rd Column are Identical Hence value of determinant is zero ∆ = 1/2 (a + b + c) × 0 ∆ = 0 So, ∆ = 0 Hence points A, B & C are collinear

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.