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)

$\sqrt{53}$

Answer 2

Let feet of perpendicular is $(2 \alpha ,3 \alpha + 2, 4 \alpha + 3)$ $\Rightarrow$ Direction ratio of the $\bot$ line is $2 \alpha - 3,3 \alpha + 3,4 \alpha - 8$. and Direction ratio of the line 2, 3, 4 are $\Rightarrow \, 2(2 \alpha -3)+3(3 \alpha + 3)+4(4 \alpha - 8)=0$ $\Rightarrow \, 29 \alpha - 29 = 0$ $\Rightarrow \, \alpha = 1$ $\Rightarrow$ Feet of $\bot$ is (2, 5, 7) $\Rightarrow$ Length $\bot$ is $\sqrt{1^2 + 6^2 + 4^2} = \sqrt{53}$