Question

The equation of the plane perpendicular to the line $\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z+1}{2}$ and passing through the point $(2,3,1)$ is

• A. $r.(\hat{i}+\hat{j}+2\hat{k})=1$
• B. $r.(\hat{i}-\hat{j}+2\hat{k})=1$
• C. $r.(\hat{i}+\hat{j}+2\hat{k})=7$
• D. None of these

Answer 1

The correct option is B $r.(\hat{i}-\hat{j}+2\hat{k})=1$

The given line is parallel to the vector $n=\hat{i}-\hat{j}+2\hat{k}$. The required plane passes through the point $(2,3,1)$ ie., $2\hat{i}+3\hat{j}+\hat{k}$
so, its equation is,
$r-(2\hat{i}-3\hat{j}+\hat{k})(\hat{i}-\hat{j}+2\hat{k})=0$
$\Rightarrow r.(\hat{i}-\hat{j}+2\hat{k})=1$