Question:

$N$ = foot of $\perp$ from $P(1,-2,3)$ on line through $(4,5,8)$ and $(1,-7,5)$. Distance of $N$ from $2x-2y+z+5=0$ is

Step-by-Step Solution

Key Concept: Direction of line: $(3,12,3)$, i.e., $(1,4,1)$. Foot: $N=(1,-7,5)+t(3,12,3)$; $\overrightarrow{PN}\cdot(1,4,1)=0$.

Distance $=9$.

Correct Answer: 3