MHT CET202120 Sep 2021Evening ShiftMathematicsVector AlgebraActual

r =-4 i -6 j -2 k is a linear combination of the vector a =- i -4 j +3 k and b =-8 i - j +3 k , then

Options

Ar = -4 3 a + 2 3 b
Br = 4 3 a + 2 3 b
Cr = -1 3 a + 2 3 b
Dr = 1 3 a - 1 3 b

Correct answer

A. r = -4 3 a + 2 3 b

Step-by-step solution

Let r=x a +y b aligned & -4 i -6 j -2 k =x(- i +4 j +3 k )+y(-8 i - j +3 k ) & =(-x-8 y) i +(4 x-y) j +(3 x+3 y) k & -x-8 y (1) & 4 x-y =-4 (2) & 3 x+3 y =-2 (3) aligned Solving (1) and (2), we get y = 2 3 and x = -4 3

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