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

Engineering

Mathematics

Plane and Its Different Forms

Question

x – 2y + 2z + 1 = 0

x – 2y + 2z + 5 = 0

x – 2y + 2z – 3 = 0

x – 2y + 2z – 1 = 0

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Equation of plane parallel to x – 2y + 2z – 5 = 0 is x – 2y + 2z = λ

Distance from origin is 1.

$\frac{| 0 + 0 + 0 - λ |}{\sqrt{1^{2} + 2^{2} + 2^{2}}} = 1$

∴ λ = ± 3

P : x – 2y + 2z = ± 3.