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JEE Main20198 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The equation of a plane containing the line of intersection of the planes 2 x - y - 4 = 0 and y + 2 z - 4 = 0 and passing through the point 1,1 , 0 is

Options

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

Correct answer

C. x - y - z = 0

Step-by-step solution

Equation of plane passing through the intersection of two given Plane 2 x - y - 4 = 0 and y + 2 z - 4 = 0 is, 2 x - y - 4 + λ   y + 2 z - 4 = 0 ⇒ 2 x + y   λ - 1 + 2 λ z - 4 - 4 λ = 0 ∵ It passes through ( 1,   1 ,   0 ) ∴       2 × 1 + λ - 1 + 0 - 4 - 4 λ = 0 ⇒ - 3 λ - 3 = 0 ⇒ λ = - 1 ∴ Equation of plane 2 x - 2 y - 2 z = 0 ⇒ x - y - z = 0

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