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KCET2016MathematicsThree Dimensional Geometry

Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane ( 5 y+8 ) ( =0 ) :

Options

  1. A( (0,- 18 5 , 2 ) )
  2. B( (0, 8 5 , 0 ) )
  3. C( ( 8 25 , 0,0 ) )
  4. D( (0,- 8 5 , 0 ) )

Correct answer

D. ( (0,- 8 5 , 0 ) )

Step-by-step solution

Given equation of plane: ( 5 y+8=0 ) So, ( N =(0,5,0) ) Equation of line passes through origin and is perpendicular to this plane is given by [ x 0 = y 5 = z 0 = ] Foot of the perpendicular is found by intersection of line with plane. So, [ x=0, y=5 , z=0 ] Now, ( 25 +8=0 ) [ = -8 25 ] Therefore, point is ( (0, -8 5 , 0 ) )

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