Ex 10.2, 19 - If a,  bare two collinear vectors, then which - Collinearity Of two vectors

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.2, 19 If and are two collinear vectors, then which of the following are incorrect: (A) = , for some scalar (B) = (C) the respective components of and are not proportional (D) both the vectors and have same direction, but different magnitudes. Given, a and b are collinear vectors Checking (A) = Let = 1 + 1 + 1 & = 3 + 3 + 3 Where & are collinear (direction ratio are proportional) b = 3 i + 3 j + 3 k = 3 (1 i + 1 j + 1 k ) = 3 a So, b = a , where = 3 is a scalar. Hence, (A) is correct Checking (B) = Since & are collinear Let = 1 i + 1 j + 1 k So, = b Hence, (B) is correct Checking (C) the respective components of a and b are not proportional Since & are collinear Let = 1 + 2 + 3 & = 4 + 8 + 12 Ratio of respective components = 1 4 , 2 8 , 3 12 = 1 4 , 1 4 , 1 4 So, respective components of a & b are proportional. Hence, (C) is correct. Checking (D) both the vectors and have same direction, but different magnitudes. Since & are collinear Let = 1 + 1 + 1 & = 2 2 2 Magnitude of = 12+12+12 = 1+1+1 = 3 Magnitude of b = 2 2+( 2)2+( 2)2 = 4+4+4 = 12 = 4 3 = 2 3 Thus, = 2 i.e.. they have different magnitudes So, a & b have different magnitudes Also, b = 2 (1 i + 1 j + 1 k ) = 2 and have opposite directions Hence, (D) is incorrect. So, D is the correct option

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