Question

The vector equation of a plane through the point $(2\hat{i}-\hat{j}-4\hat{k})$ and parallel to the plane $\overrightarrow{r}$ .$(4\hat{i}-12\hat{j}-3\hat{k})-7=0$ is

• A. $\overrightarrow{r}.(4\hat{i}-12\hat{j}-3\hat{k})=0$
• B. $\overrightarrow{r}.(4\hat{i}-12\hat{j}-3\hat{k})=32$
• C. $\overrightarrow{r}.(4\hat{i}-12\hat{j}-3\hat{k})=12$
• D. None of the above

Answer 1

Answer: (B)

$\overrightarrow{r}.(4\hat{i}-12\hat{j}-3\hat{k})=32$

Equation of a plane can be written as

$\overrightarrow{n}.(x-x_0)=0$ where n is normal vector to the plane.

$\Rightarrow (4\hat{i}-12\hat{j}-3\hat{k}).(\overrightarrow{r}-2\hat{i}-\hat{j}-4\hat{k})=0$

$\Rightarrow \overrightarrow{r}.(4\hat{i}-12\hat{j}-\hat{k})=32$