Q. The perpendicular distance, of the line $\frac{x-1}2=\frac{y+2}{-1}=\frac{z+3}2$ from the point $P(2,-10,1)$, is :
A) 6
B) $5\sqrt2$
C) $4\sqrt3$
D) $3\sqrt5$
Explanation
[Solution by Dr. Abubacker] Take $A(1,-2,-3)$ on the line, $\vec d=(2,-1,2)$, $|\vec d|=3$, and $\vec{AP}=(1,-8,4)$. $\vec{AP}\times\vec d=(-12,6,15)$ with magnitude $\sqrt{405}$. Distance $=\frac{\sqrt{405}}3=\sqrt{45}=3\sqrt5$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.