Question

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

• A. $\frac{2}{3}$
• B. $\frac{4}{3}$
• C. $\frac{5}{3}$
• D. $\frac{7}{3}$

Answer 1

The correct option is C $\frac{5}{3}$

Given planes can be written as,

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

and $\overrightarrow{r}.(2\hat{i}-3\hat{j}+6\hat{j})=-\frac{20}{3}$, divide by $3$.

Clearly both the planes are parallel.

Hence, distance between them is $=\frac{5+\frac{20}{3}}{\sqrt{2^2+3^2+6^2}}=\frac{5}{3}$