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MHT CET202016 Oct 2020Morning ShiftMathematicsThree Dimensional GeometryActual

If the foot of perpendicular drawn from the origin to the plane is (3,2,1) , then the equation of plane is

Options

  1. A3x+2y-z=12
  2. B3x+2y-z=14
  3. C3x+2y+z=14
  4. D3x-2y-z=12

Correct answer

C. 3x+2y+z=14

Step-by-step solution

(B) Let P(3,2,1) be the foot of the perpendicular from the origin to the plane. aligned OP &= n =3 i +2 j + k and P &=|3 i +2 j + k |= 3²+2²+1² = 14 n &= 3 i +2 j + k 14 aligned The vector equation of the plane is aligned &(x i +y j +z k ) (3 i +2 j + k ) 14 = 14 & 3 x+2 y+z=14 3 x+2 y+z-14=0 aligned

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