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JEE Main2015MathematicsThree Dimensional GeometryActual

The equation of the plane containing the line of intersection of 2 x - 5 y + z = 3 ; x + y + 4 z = 5 , and parallel to the plane, x + 3 y + 6 z = 1 , is

Options

  1. A2 x + 6 y + 1 2 z = - 1 3
  2. B2 x + 6 y + 1 2 z = 1 3
  3. Cx + 3 y + 6 z = - 7
  4. Dx + 3 y + 6 z = 7

Correct answer

D. x + 3 y + 6 z = 7

Step-by-step solution

Any plane containing the line of intersection of 2 x - 5 y + z = 3 ,   x + y + 4 z = 5 will be of the form 2 x - 5 y + z - 3 + λ x + y + 4 z - 5 = 0 2 + λ x - 5 - λ y + 1 + 4 λ z - 3 + 5 λ = 0 It is parallel to plane x + 3 y + 6 z = 1 ⇒    2 + λ 1 = λ - 5 3 = 1 + 4 λ 6 ≠ 3 + 5 λ 1 2 + λ 1 = λ - 5 3    ⇒    6 + 3 λ = λ - 5 2 λ = - 1 1 λ = - 1 1 2 ∴ Required plane is 2 x

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