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MHT CET202523 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

If the foot of the perpendicular drawn from the origin to a plane is P (2,-1,4) , then the equation of the plane is

Options

  1. A2 x+y+4 z-19=0
  2. Bx+y+z-5=0
  3. C2 x-2 y-3 z+6=0
  4. D2 x-y+4 z-21=0

Correct answer

D. 2 x-y+4 z-21=0

Step-by-step solution

Key concept: Since the perpendicular from the origin meets the plane at (2, -1, 4) , the vector OP is normal to the plane, with components (2, -1, 4) . Using the point-normal form, the plane equation becomes 2(x - 2) - 1(y + 1) + 4(z - 4) = 0 . Simplifying, 2x - 4 - y - 1 + 4z - 16 = 0 , so 2x - y + 4z - 21 = 0 . This corresponds to option D. The final answer is D .

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