Question

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

• A. x-2y +2z -3 =0
• B. x -2y +2z +1 =0
• C. x -2y +2z -1 =0
• D. x -2y +2z +5 =0

Answer 1

The correct option is A x-2y +2z -3 =0

Equation of plane parallel to $x-2y+2z-5=0$ is $x-2y+2z+k=0$
Also, the plane is of unit distance from the origin.
$\therefore \frac{|k|}{\sqrt{1+4+4}}=1\Rightarrow |k|=3\Rightarrow k=\pm 3$

$x-2y+2z-3=0$ satisfies the condition.