JEE Main · 2012 · 29 Apr 2012 · Offline · Three Dimensional Geometry

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

(A) $x - 2 y + 2 z - 3 = 0$ ✓ Correct
(B) $x - 2 y + 2 z + 1 = 0$
(C) $x - 2 y + 2 z - 1 = 0$
(D) $x - 2 y + 2 z + 5 = 0$

Answer: (A)

Solution

A plane parallel to

x - 2 y + 2 z - 5 = 0

must have the form

x - 2 y + 2 z + k = 0

. Its distance from the origin is

\frac{∣ k ∣}{1 ^{2} + ( - 2 ) ^{2} + 2 ^{2}} = \frac{∣ k ∣}{3}

, and setting this equal to

1

gives

∣ k ∣ = 3

. The choice

k = - 3

produces the plane

x - 2 y + 2 z - 3 = 0

, which is the one that appears among the choices.

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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