Question

Distance between two parallel planes $2x+y+2z=8$ and $4x+2y+4z+5=0$ is :

• A. $\frac{3}{2}$
• B. $\frac{5}{2}$
• C. $\frac{7}{2}$
• D. $\frac{9}{2}$

Answer 1

The correct option is C $\frac{7}{2}$

$2x+y+2z=\mathrm{8...}\left(1\right)$
$2x+y+2z+\frac{5}{2}=\mathrm{0...}\left(2\right)$
Distance between parallel lines $\left(1\right)$ and $\left(2\right)$ is
$D=\left|\frac{-8-\frac{5}{2}}{\sqrt{2^2+1^2+2^2}}\right|$
$=\left|\frac{-\frac{21}{2}}{3}\right|$
$=\frac{7}{2}$