Question

The equation of the plane which is parallel to the plane $x - 2 y + 2 z = 5$ and whose distance from the point $( 1,2,3 )$ is 1, is

• A. $x - 2 y + 2 z = 3$
• B. $x - 2 y + 2 z + 3 = 0$
• C. $x - 2 y + 2 z = 6$
• D. $x - 2 y + 2 z + 6 = 0$

Answer 1

Answer: (C)

$x - 2 y + 2 z = 6$

Answer 2

Equation of plane parallel to $x - 2 y + 2 z = 5$ is

$x - 2 y + 2 z + k = 0$ …..(i)

Now, according to question, $\frac { 1 - 4 + 6 + k } { \sqrt { 9 } } = \pm 1$

or $k + 3 = \pm 3 \Rightarrow k = 0$ or – 6

$\therefore x - 2 y + 2 z - 6 = 0$ or $x - 2 y + 2 z = 6$.