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AP EAMCET202421 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let be the plane that passes through the point (-2,1,-1) and parallel to the plane 2 x-y+2 z=0 . Then the foot of perpendicular drawn from the point (1,2,1) to the plane is

Options

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

Correct answer

D. (-1,3,-1)

Step-by-step solution

Equation of plane parallel to 2 x-y+2 z=0 is 2 x-y+2 z+k=0 It also passes through (-2,1,-1) aligned & -4-1-2+k=0 k=7 & 2 x-y+2 z+7=0 aligned Let (a, b, c) be the foot of perpendicular from (1,2,1) to aligned & a-1 2 = b-2 -1 = c-1 2 = & a=2 +1, b=- +2, c=2 +1 aligned (a, b, c) also lies in 2(2 +1)+ -2+2(2 +1)+7=0 =-1 So, (a, b, c)=(-1,3,-1)

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