Q59 / 125 · BITSAT 2019 · Mathematics

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

Solution

Equation of plane parallel to the plane

$x - 2 y + 2 z - 5 = 0$ is $x - 2 y + 2 z + λ = 0$

Since, this plane is unit distance from origin

$∴ 1 = |\frac{λ}{\sqrt{1 + 4 + 4}}|$

$| λ | = 3 \Rightarrow λ = \pm 3$

$∴$ Equation of plane is

$x - 2 y + 2 z = 3$

Hence, the correct answer is option: 'A'.