An equation of a plane parallel to the plane x - 2y + 2z - 5 = 0 and at a unit distance from the origin is: - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

A plane parallel to x - 2 y + 2 z - 5 = 0 is x - 2 y + 2 z + k = 0 .The distance from origin (0, 0, 0) to this plane is given by: d = \frac{∣0 - 2 ( 0 ) + 2 ( 0 ) + k ∣}{1 ^{2} + ( - 2 ) ^{2} + 2 ^{2}} 1 = \frac{∣ k ∣}{1 + 4 + 4} ⟹ 1 = \frac{∣ k ∣}{3} ∣ k ∣ = 3 ⟹ k = \pm 3 The possible equations are x - 2 y + 2 z + 3 = 0 and x - 2 y + 2 z - 3 = 0 .Comparing with options, x - 2 y + 2 z - 3 = 0 is correct.

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

x - 2 y + 2 z - 3 = 0

x - 2 y + 2 z + 1 = 0

x - 2 y + 2 z - 1 = 0

x - 2 y + 2 z + 5 = 0

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