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MHT CET202611 April 2026Evening ShiftMathematicsVector AlgebraActual

If a = i + j + k , b = i - j + 2 k and c = x i + (x - 2) j - k are three vectors in which c lies in the plane of a and b , then x =

Options

  1. A0
  2. B1
  3. C-4
  4. D-2

Correct answer

D. -2

Step-by-step solution

Since c lies in the plane of a and b , the vectors a , b , and c are coplanar. Therefore, their scalar triple product is zero: [ a b c ] = 0 vmatrix 1 & 1 & 1 1 & -1 & 2 x & x - 2 & -1 vmatrix = 0 Expanding the determinant along the first row: 1((-1)(-1) - 2(x - 2)) - 1(1(-1) - 2x) + 1(1(x - 2) - (-1)x) = 0 1(1 - 2x + 4) - 1(-1 - 2x) + 1(x - 2 + x) = 0 (5 - 2x) + (1 + 2x) + (2x - 2) = 0 4 + 2x = 0 2x = -4 x = -2 Answer: -2

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