Question

Find the distance between the parallel planes $\overrightarrow{r}.(2\hat{i}-3\hat{j}+6\hat{k})=5$ and$\overrightarrow{r}.(6\hat{i}-9\hat{j}+18\hat{k})+20=0.$

Answer 1

Distance between the two parallel plane

$\overrightarrow{r}(2\hat{i}-3\hat{j}+6\hat{k})=5$

and $\overrightarrow{r}(6\hat{i}-9\hat{j}+18\hat{k})+20=0$

$d=\left|\frac{5-\frac{20}{3}}{\sqrt{2^2+3^2+6^2}}\right|=\left|\frac{\frac{-5}{3}}{\sqrt{49}}\right|$

$=\frac{5}{21}$units