Question

The equation of the plane mid-parallel to the planes $2x-3y+6z-7=0$ and $2x-3y+6z+7=0$ is

• A. $2x-3y+6z=6$
• B. $2x-3y+6z=0$
• C. $2x-3y+6z=14$
• D. $2x-3y+6z=8$

Answer 1

The correct option is B $2x-3y+6z=0$

Let the equation of the mid-parallel plane be
$2x-3y+6z+k=0$
Distance of the above plane will be equal to both the planes
$\Rightarrow \left|\frac{k+7}{\sqrt{2^2+3^2+6^2}}\right|=\left|\frac{k-7}{\sqrt{2^2+3^2+6^2}}\right|$
$\Rightarrow |k+7|=|k-7|$
$\Rightarrow k+7=k-7$ or $k+7=-k+7$
$\therefore k=0$
$\Rightarrow$ Equation of mid-parallel plane is $2x-3y+6z=0$