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KCET2022MathematicsThree Dimensional Geometry

The coordinates of foot of the perpendicular drawn from the origin to the plane 2 x-3 y+4 z=29 are

Options

  1. A(2,3,4)
  2. B(2,-3,-4)
  3. C(2,-3,4)
  4. D(-2,-3,4)

Correct answer

C. (2,-3,4)

Step-by-step solution

Given, equation of plane is 2 x-3 y+4 z=29 Since, O P is perpendicular to the plane 2 x-3 y+4 z=29 Therefore, Direction Ratios of O P will be 2,-3,4 . Equation of line O P will be x-0 2 = y-0 -3 = z-0 4 = ( say ) Coordinates of P will be (2 ,-3 , 4 ) . P lies on plane, so 2(2 )-3(-3 )+4(4 )=29 4 +9 +16 =29 =1 Coordinates of P will be (2,-3,4) .

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