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Let P be the image of the point 3,1 , 7 with respect to the plane x - y + z = 3 . The equation of the plane passing through P and parallel to x - 2 y + 3 z = 7 is

Options

  1. Ax - 2 y + 3 z = 2
  2. B2 x - 4 y + 6 z = 7
  3. Cx + 2 y - 6 z + 2 = 0
  4. Dx - 2 y + 3 z + 2 = 0

Correct answer

D. x - 2 y + 3 z + 2 = 0

Step-by-step solution

Image of 3,1 , 7 w.r.t. plane x - y + z - 3 = 0 is x - 3 1 = y - 1 - 1 = z - 7 1 = - 2 6 3 = - 4 x = - 1 , y = 5 , z = 3 So, image is - 1,5 , 3 Equation of the plane through P and parallel to x - 2 y + 3 z = 7 is 1 x + 1 - 2 y - 5 + 3 z - 3 = 0 x + 1 - 2 y + 10 + 3 z - 9 = 0 x - 2 y + 3 z + 2 = 0

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