Question

Find the vector equation of the plane which is at a distance of $5$ units from the origin and which in normal to the vector $2\hat{i}+\hat{j}+2\hat{k}$

Answer 1

Vector equation

$\overrightarrow{r}.\hat{n}=d$

$d=5$

$\hat{n}=\frac{2i+j+2k}{\sqrt{2^2+2^2+1}}=\frac{1}{3}(2\hat{i}+\hat{j}+2\hat{k})$

$\Rightarrow \overrightarrow{r}.\frac{1}{3}(2\hat{i}+\hat{j}+2\hat{k})=5$