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MHT CET2019Evening ShiftMathematicsThree Dimensional GeometryActual

Equations of planes parallel to the plane x - 2 y + 2 z + 4 = 0 which are at a distance of one unit from the point 1,2 , 3 are …..

Options

  1. Ax + 2 y + 2 z = - 6 , x + 2 y + 2 z = 5
  2. Bx - 2 y - 6 = 0 , x - 2 y + z = 6
  3. Cx - 2 y + 2 z = 6 , x + 2 y + 2 z = 0
  4. Dx - 2 y + 2 z = 0 , x - 2 y + 2 z - 6 = 0

Correct answer

D. x - 2 y + 2 z = 0 , x - 2 y + 2 z - 6 = 0

Step-by-step solution

Given equation of plane x - 2 y + 2 z + 4 = 0 ….(i) Equation of plane parallel (ii) from point (1, 2, 3) is 1 unit ∴ 1 1 - 2 2 + 2 3 + k 1 2 + - 2 2 + 2 2 = 1 ⇒ 1 - 4 + 6 + k 1 + 4 + 4 = 1 ⇒ 3 + k 9 = 1 ⇒ 3 + k = 3 ⇒ 3 + k = ± 3 ∴ x - 2 y + 2 z + 0 = 0 and x - 2 y + 2 z - 6 = 0 ⇒ x - 2 y + 2 z = 0 and x - 2 y + 2 z - 6 = 0

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