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MHT CET20244 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be a plane passing through the points (2,1,0),(4,1,1) and (5,0,1) and R be the point (2,1,6) . Then image of R in the plane P is

Options

  1. A(6,5,2)
  2. B(4,3,2)
  3. C(6,5,-2)
  4. D(3,4,-2)

Correct answer

C. (6,5,-2)

Step-by-step solution

Equation of the plane passing through (2,1,0) , (4,1,1) and (5,0,1) is aligned & | array lll x-2 & y-1 & z-0 4-2 & 1-1 & 1-0 5-2 & 0-1 & 1-0 array |=0 & x+y-2 z=3 aligned R ^ (x, y, z ) is image of R (2,1,6) w.r.t. to plane x+y-2 z=3 x-2 1 = y-1 1 = z-6 -2 = -2[2+1-2(6)-3] 1+1+4 x-2 1 = y-1 1 = z-6 -2 =4 x=6, y=5, z =-2 R ^ (x, y, z ) (6,5,-2)

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