Question

The length of the perpendicular drawn from the point $(3,-1,11)$ to the line $\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ is

• A. $\sqrt{66}$
• B. $\sqrt{29}$
• C. $\sqrt{33}$
• D. $\sqrt{53}$

Answer 1

Answer: (D)

Coordinates of $Q$ are $(2\lambda ,-3\lambda +2,4\lambda +3)$
Dr's of $PQ$ are $(2\lambda -3,3\lambda +3,4\lambda -8)$
Dr's Of line $(2,3,4)$
$\Rightarrow 2(2\lambda -3)+3(3\lambda +3)+4(4\lambda -8)=0$
$\Rightarrow 29\lambda -29=0$
$\Rightarrow \lambda =1$
$Q=(2,5,7)$
$\because |PQ|=\sqrt{53}$