Ex 10.3, 16 - Chapter 10 Class 12 Vector Algebra

Transcript

Ex 10.3, 16 (Introduction) Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, 1) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three vectors collinear i.e. + = Ex 10.3, 16 Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, 1) are collinear. 3 points A, B, C are collinear if i.e. + = A (1, 2, 7) B (2, 6, 3) C (3, 10, 1) = (2 1) + (6 2) + (3 7) = 1 + 4 4 = (3 2) + (10 6) + ( 1 3) = 1 + 4 4 = (3 1) + (10 2) + ( 1 7) = 2 + 8 8 Magnitude of = 12+42+ 4 2 = 1+16+16 = 33 Magnitude of = 12+42+ 4 2 = 1+16+16 = 33 Magnitude of = 22+82+ 8 2 = 4+64+64 = 132 = 4 33 = 2 33 Thus, + = 33 + 33 = 2 33 = Thus, A, B and C are collinear.