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MHT CET202019 Oct 2020Evening ShiftMathematicsVector AlgebraActual

a and b are non-collinear vectors. If p =(2 x+1) a - b and q =(x-2) a + b are collinear vectors, then x=

Options

  1. A-3
  2. B1 3
  3. C- 1 3
  4. D3

Correct answer

B. 1 3

Step-by-step solution

(A) The vector q is non-zero since the coefficient in b is different from zero and so the vectors q and p are collinear if for some number y we have p = c q that is (2 x+1) a - b =y[(x-2) a + b ] (2 x+1)=y(x-2) and -1=y y=-12 x+1=-(x-2) 3 x=1 x= 1 3

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