Question

The distance of the point $(1,1,1)$ from the plane passing through the point $(-1,-2,-1)$ and whose normal is perpendicular to both the lines $L_1$ and $L_2$ is _________.

• A. $\frac{2}{\sqrt{75}}$
• B. $\frac{7}{\sqrt{75}}$
• C. $\frac{13}{\sqrt{75}}$
• D. $\frac{23}{\sqrt{75}}$

Answer 1

The correct option is C $\frac{13}{\sqrt{75}}$

The given equations of line are

$L_1:\frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$ and $L_2:\frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}$

Plane is given by $(x+1)-7(y+2)+5(z+1)=0$

$\Rightarrow x+7y-5z+10=0$

$\Rightarrow$ distance $=\frac{1+7-5+10}{\sqrt{75}}=\frac{13}{\sqrt{75}}$