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BITSAT2019MathematicsThree Dimensional GeometryActual

An equation of plane parallel to plane x - 2 y + 2 z - 5 = 0 and at a unit distance from the origin is

Options

  1. Ax - 2 y + 2 z = 3
  2. Bx - 2 y + 2 z + 1 = 0
  3. Cx - 2 y + 2 z - 1 = 0
  4. Dx - 2 y + 2 z + 5 = 0

Correct answer

A. x - 2 y + 2 z = 3

Step-by-step solution

Equation of plane parallel to the plane x - 2 y + 2 z - 5 = 0 is x - 2 y + 2 z + λ = 0 Since, this plane is unit distance from origin ∴   1 = λ 1 + 4 + 4 | λ | = 3 ⇒ λ = ± 3 ∴ Equation of plane is x - 2 y + 2 z = 3

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