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MHT CET202520 Apr 2025Evening ShiftMathematicsVector AlgebraActual

If the points A (1,1,2), B (2,1, p ), C (1,0,3) and D (2,2,0) are coplanar then the value of p is

Options

  1. A0
  2. B-1
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

Four points are coplanar if the scalar triple product of vectors from one point to the other three is zero. From point A(1,1,2), the vectors are: AB = (1, 0, p-2) AC = (0, -1, 1) AD = (1, 1, -2) The scalar triple product [ AB AC AD ] equals the determinant: vmatrix 1 & 0 & p-2 0 & -1 & 1 1 & 1 & -2 vmatrix = 0 Evaluating the determinant yields: 1 (2 - 1) + (p-2) (0 + 1) = 0 1 + p - 2 = 0 p = 1 The points are coplanar when p = 1 , corresponding to option C.

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