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MHT CET202123 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The coordinates of the foot of the perpendicular drawn from the origin to the plane 2 x+y-2 z=18 are

Options

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

Correct answer

A. (4,2,-4)

Step-by-step solution

2 x+y-2 z=18 Dividing both sides (2)^2+(1)^2+(-2)^2 =3 , we get ( 2 3 ) x + ( 1 3 ) y - ( 2 3 ) z =6 Hence length of perpendicular from origin to the plane is 6 . Therefore coordinates of foot of perpendicular are [ ( 2 3 )(6), ( 1 3 )(6), ( -2 3 )(6) ] i.e. (4,2,-4)

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