Question

The distance between the parallel planes given by the equations, $\overrightarrow{r}.(2\hat{i}-2\hat{j}+\hat{k})+3=0$ and $\overrightarrow{r}.(4\hat{i}-4\hat{j}+2\hat{k})+5=0$ is-

• A. $1/2$
• B. $1/3$
• C. $1/4$
• D. $1/6$

Answer 1

The correct option is D $1/6$

Planes are $2i-2j+k+3=0,4i-4j+2k+5=0,2i-2j+k+5/2=0$

distance between them is $=\frac{|c_1-c_2|}{\sqrt{a^2+b^2+c^2}}=\frac{|3-\frac{5}{2}|}{\sqrt{2^2+2^2+1^2}}=\frac{1}{6}$