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) $
$\because|P Q|=\sqrt{53}$