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MHT CET202526 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

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

Options

  1. Ax+y-2 z+6=0
  2. B2 x+y+z+1=0
  3. Cx+y+2 z-2=0
  4. Dx-y-z+2=0

Correct answer

A. x+y-2 z+6=0

Step-by-step solution

The foot of the perpendicular from the origin O(0,0,0) to the plane is P(-1,-1,2) . Since OP is perpendicular to the plane, the normal vector n is proportional to OP = -1, -1, 2 . The plane passing through P with this normal vector satisfies -1(x + 1) -1(y + 1) + 2(z - 2) = 0 . Expanding and simplifying: -x - 1 - y - 1 + 2z - 4 = 0 -x - y + 2z - 6 = 0 Multiplying by -1 yields x + y - 2z + 6 = 0 , which corresponds to option A. Final answer: A

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