The distance between the parallel planes, $\vec{r}.(2\hat{i}-3\hat{j} + 6 \hat{k}) = 5 $ and $\vec{r}.(6\hat{i} - 9 \hat{j}+18\hat{k})+20 = 0 ,$ is
Answer & explanation
Correct answer: option 2
The equations of two planes are
$\vec{r}.(2\hat{i}-3\hat{j} + 6 \hat{k}) = 5 $ and $\vec{r}.(2\hat{i} - 3 \hat{j}+6\hat{k})=-\frac{20}{3} $
∴ Distance between the planes $= \frac{|5-(-\frac{20}{3})|}{|2\hat{i}-3\hat{j}+6\hat{k}|}=\frac{5}{3}$