Question

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

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

Answer 1

The correct option is C $x-2y+2z=6$

As the plane is at unit distance from the point $\left(1,2,3\right)$, then,

$\left|\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}\right|=d_1$

$\left|\frac{1-4+6+d}{\sqrt{1+4+4}}\right|=1$

$\frac{3+d}{3}=\pm 1$

$d=-6$

So, the equation of plane is $x-2y+2z=6$.