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

$\frac{7}{2}$

Given planes are
$2x+y+2z-8=0and2x+y+2z+\frac{5}{2}=0\therefore Distancebetweentwoplanes=\frac{|c_1-c_2|}{\sqrt{a^2+b^2+c^2}}=\left|\frac{-8-\frac{5}{2}}{\sqrt{2^2+1^2+2^2}}\right|=\frac{\frac{21}{2}}{3}=\frac{7}{2}$