Find the distance between the planes vector(r) . (2i - 3j + 6k) - 4 = 0

Question

Find the distance between the planes

\(\vec{r}.(2\hat{i}-3\hat{j}+6\hat{k}) - 4=0\) and \(\vec{r}.(6\hat{i}-9\hat{j}+18\hat{k}) + 30=0\)

Answer 1

Given two planes are

Given planes may be written in cartesian form as

Let P \((x_1, y_1, z_1)\) be a point on plane (i)

The length of the perpendicular from P \((x_1, y_1, z_1)\) to plane (ii)