First slide

Planes in 3D

Question

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

Easy

A

$x - 2 y + 2 z - 7 = 0$
B

$x - 2 y + 2 z + 5 = 0$
C

$x - 2 y + 2 z - 3 = 0$
D

$x - 2 y + 2 z + 1 = 0$

Solution

The required plane is $x - 2 y + 2 z + k = 0$ . The distance to the plane from origin = 1
$\Rightarrow \frac{| k |}{\sqrt{1 + 4 + 4}} = 1 \Rightarrow k = \pm 3$

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