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JEE Advanced2015MathematicsThree Dimensional GeometryActual

In R 3 , consider the planes P 1 : y = 0 and P 2 : x + z = 1 . Let P 3 , be a plane, different from P 1 and P 2 , which passes through the intersection of P 1 and P 2 . If the distance of the point 0 , 1 , 0 , from P 3 , is 1 , and the distance of a point ( α , β , γ ) , from P 3 , is 2 , then which of the following relations is (are) true ?

Options

  1. A2 α + β + 2 γ + 2 = 0
  2. B2 α - β + 2 γ + 4 = 0
  3. C2 α + β - 2 γ - 10 = 0
  4. D2 α - β + 2 γ - 8 = 0

Correct answer

B. 2 α - β + 2 γ + 4 = 0

Step-by-step solution

P 1 : y = 0 P 2 : x + z = 1 P 3 : y + λ x + z - 1 = 0 ∴ β + λ α + γ - 1 1 + 2 λ 2 = ± 2 ∴ β + λ α + γ - 1 = ± 2 1 + 2 λ 2 1 - λ 1 + 2 λ 2 = ± 1 λ = - 2 λ ≠ 0 ∴ β - 2 α + γ - 1 = ± 2 3 2 α - β + 2 γ + 4 = 0 or 2 α - β + 2 γ - 8 = 0 .

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