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KCET2019MathematicsThree Dimensional Geometry

Foot of the perpendicular drawn from the point ( (1,3,4) ) to the plane ( 2 x-y+z+3=0 ) is

Options

  1. A( (0,-4,-7) )
  2. B((-3,5,2) )
  3. C((-1,4,3) )
  4. D( (1,2,-3) )

Correct answer

C. ((-1,4,3) )

Step-by-step solution

(C) The dr's of PA are ( x₁-1, y₁-3, z₁-4 ) The dr's ( n ) are ( 2,-1,1 ) The dr's of PA and n are parallel [ array l x₁-1 2 = y₁-3 -1 = z₁-4 1 = x₁=2 +1, y₁=- +3, z₁= +4 A=(2 +1,- +3, +4) lies on 2 x-y+z+3=0 -4 +2- -3- +4+3=0 6 =-6 =-1 P=(-1,4,3) array ]

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