Question

Find the distance between the parallel planes $\overrightarrow{r}.(2\hat{i}-\hat{j}-2\hat{k})=6$ and $\overrightarrow{r}.(6\hat{i}-3\hat{j}-6\hat{k})=27$

Answer 1

the two planes are $\Rightarrow$

$\overrightarrow{r}.(2\hat{i}-\hat{j}-2\hat{k})=6$

and

$\overrightarrow{r}.(2\hat{i}-\hat{j}-2\hat{k})=9$

$\therefore$ the distance between these two planes is $\frac{9-6}{\sqrt{(2{)}^2+(-1{)}^2+(-2{)}^2}}=\frac{3}{3}=1$ unit.