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MHT CET202618 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

If the equation of a plane passing through A(1, p, 2) , B(3, 2, 4) and parallel to the z axis, is 3x - 2y - q = 0 , then

Options

  1. Ap = -1, q = 5
  2. Bp = 1, q = -5
  3. Cp = -2, q = -5
  4. Dp = 2, q = -5

Correct answer

A. p = -1, q = 5

Step-by-step solution

The equation of the plane is given as 3x - 2y - q = 0 . Since the plane passes through the point B(3, 2, 4) , its coordinates must satisfy the plane equation. Substituting x = 3 and y = 2 : 3(3) - 2(2) - q = 0 9 - 4 - q = 0 q = 5 The plane also passes through the point A(1, p, 2) . Substituting x = 1 , y = p , and q = 5 into the plane equation: 3(1) - 2(p) - 5 = 0 3 - 2p - 5 = 0 -2p = 2 p = -1 Thus, p = -1 and q = 5 . Answer: p = -1, q = 5

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