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JEE Advanced2016MathematicsThree Dimensional GeometryActual

Let P be the image of the point ( 3 , 1 , 7 ) with respect to the plane x - y + z = 3 . Then the equation of the plane passing through P and containing the straight line x 1 = y 2 = z 1 is

Options

  1. Ax + y - 3 z = 0
  2. B3 x + z = 0
  3. Cx - 4 y + 7 z = 0
  4. D2 x - y = 0

Correct answer

C. x - 4 y + 7 z = 0

Step-by-step solution

Let F be mid point of AP Line AP : x - 3 1 = y - 1 - 1 = z - 7 1 = λ ⇒ F 3 + λ , 1 - λ , λ + 7 lies in the plane ∴ 3 + λ - 1 - λ + λ + 7 = 3 3 λ = - 6 ⇒ λ = - 2 ⇒ F 1 , 3 , 5 ⇒ P - 1 , 5 , 3 (using mid point F ) So required plane (containing line x 1 = y 2 = z 1 & passing through P - 1 , 5 , 3 ) is x - 0 y - 0 z - 0 1 2 1 - 1 5 3 = 0 ∴ x - 4 y + 7 z = 0

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