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BITSAT2019MathematicsThree Dimensional GeometryActual

The equation of plane containing line x - y = 1 , z = 1 and parallel to x 2 - z 3 = 1 , y = 3 is

Options

  1. A3 x + 3 y - 2 z = 1
  2. B3 x - 3 y - 2 z = 1
  3. C3 x + 3 y + 2 z = 1
  4. D3 x + 3 y + 2 z = - 1

Correct answer

B. 3 x - 3 y - 2 z = 1

Step-by-step solution

Equation of plane containing line x - y - 1 = 0 and z - 1 = 0 is ( x - y - 1 ) + λ ( z - 1 ) = 0 ⇒   x - y + λ z - 1 - λ = 0 . . . ( i ) Since, this plane is parallel to line x 2 - z 3 = 1 and y = 3 x - 2 2 = y - 3 0 = z 3 . . . ( ii ) ∴   2 ( 1 ) + ( 0 ) ( - 1 ) + 3 ( λ ) = 0 ⇒   λ = - 2 / 3 Putting the value of λ in Eq. ( i ) , we get x - y - 2 3 z - 1 + 2 3 = 0 ⇒ 3 x - 3 y - 2 z = 1

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