Q131 / 225 · JEE Main 2004 · Mathematics

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

A
$\frac{3}{2}$
B
$\frac{5}{2}$
Correct answer
C
$\frac{7}{2}$
D
$\frac{9}{2}$

Solution

Given planes are $$ 2 x+y+2 z-8=0,4 x+2 y+4 z+5=0 \Rightarrow 2 x+y+2 z+5 / 2=0 $$ Distance between planes $=\frac{\left|d_1-d_2\right|}{\sqrt{a^2+b^2+c^2}}=\frac{|-8-5 / 2|}{\sqrt{2^2+1^2+2^2}}=\frac{7}{2}$

Hence, the correct answer is option: 'C'.

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