Question

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

Answer 1

$\begin{array}{c}Wehave\\ 2x+y+27=8\\ and,4x+2y+47=-5\\ \Rightarrow 2x+y+27=\frac{-5}{2}\\ Now,\\ Dis\tan ced=\frac{\left|8+\frac{5}{2}\right|}{\sqrt{{\left(2\right)}^2+{\left(1\right)}^2+{\left(2\right)}^2}}\\ =\frac{\frac{21}{2}}{\sqrt{3}}=\frac{21}{2\times 3}=\frac{7}{2}\\ Hence,thedis\tan cebetweentwogivenlinesare\frac{7}{2}.\end{array}$