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KCET2023MathematicsThree Dimensional Geometry

If (2,3,-1) is the foot of the perpendicular from (4,2,1) to a plane, then the equation of the plane is

Options

  1. A2 x+y+2 z-1=0
  2. B2 x-y+2 z=0
  3. C2 x+y+2 z-5=0
  4. D2 x-y+2 z+1=0

Correct answer

D. 2 x-y+2 z+1=0

Step-by-step solution

Since, the line joining the two points is perpendicular to the plane, it's DR's will given the normal to the plane. DR's of the normal =(4-2,2-3,1+1)=(2,-1,2) Hence, a=2, b=-1 and c=2 Since, the plane passes through (2,3,-1) . aligned & d=2(2)+3(-1)-1(2) & d=-1 aligned Hence, the required equation of plane is 2 x-y+2 z=-1

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