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

The correct option is D $7$

Let us take a point on line $(3\lambda +6,2\lambda +7,-2\lambda +7)$.
Direction ratio's of line which is perpendicular to given line
$(3\lambda +6-1,2\lambda +7-2,-2\lambda +7-3)$
$(3\lambda +5,2\lambda +5,-2\lambda +4)$
and the direction ratio's of given line are 3,2,-2
These two lines are perpendicular, so$(3\lambda +5)\ast 3+(2\lambda +5)\ast 2+(-2\lambda +4)+(-2)=0$
$\lambda =-1$
So, point is $(2,4,6)$
So distance between $(3,5,9)$ and $(1,2,3)$ is $7$. (by distance formula)