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JEE Main202226 Jun 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If the plane 2 x + y - 5 z = 0 is rotated about its line of intersection with the plane 3 x - y + 4 z - 7 = 0 by an angle of π 2 , then the plane after the rotation passes through the point

Options

  1. A2 , - 2 , 0
  2. B- 2 , 2 , 0
  3. C1 , 0 , 2
  4. D- 1 , 0 , - 2

Correct answer

C. 1 , 0 , 2

Step-by-step solution

Given equation of plane, P 1 : 2 x + y - 5 z = 0   and P 2 : 3 x - y + 4 z - 7 = 0 We know that equation of family of planes P 1 and P 2 is given by, P : P 1 + λ P 2 ∴ P : 2 + 3 λ x + 1 - λ y + - 5 + 4 λ z - 7 λ = 0 ∵ P ⊥ P 1    ∴ 4 + 6 λ + 1 - λ + 25 - 20 λ = 0 ⇒ λ = 2 So, equation of plane P : 8 x - y + 3 z - 14 = 0 It passes through the point 1 , 0 , 2

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