Question

The length of the perpendicular drawn from $(1,2,3)$ to the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$ is

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

Answer: (D)

Let $P$ be the point $(1,2,3)$ and $PN$ be the length of the perpendicular from $P$ on the given line.
Coordinates of point $N$ are $\left(3\lambda +6,2\lambda +7,-2\lambda +7\right)$
Now $PN$ is perpendicular to the given line or vector
$3\vec{i}+2\vec{j}-2\vec{k}.$ Thus,
$3\left(3\lambda +6-1\right)+2\left(2\lambda +7-2\right)-2\left(-2+7-3\right)=0$
or $\lambda =-1$
Then, point $N$ is $(3,5,9)$
$\Rightarrow PN=7$