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

Answer 1

Answer: (C)

Let feet of perpendicular is
$(2Î\pm ,3Î\pm +2,4Î\pm +3)$
$⇒$ Direction ratio of the $âŠ\yen$ line is
$2Î\pm −3,3Î\pm +3,4Î\pm −8$. and
$⇒$ Direction ratio of the line are $2,3,4$
$⇒2(2Î\pm −3)+3(3Î\pm +3)+4(4Î\pm −8)=0$
$⇒Î\pm =1$
$⇒$ Feet of $âŠ\yen$ is $(2,5,7)$
$⇒$ Length $âŠ\yen$ is $\sqrt{1^2+6^2+4^2}=\sqrt{53}$