Question

The foot of the perpendicular of P(2, -3, 1) on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-2}{-1}$ is Q. If the DRs of the line segment joining P and Q is l, m, n, then .

• A. 2l+3m+n = 1
• B. 2l+3m-n = 0
• C. $\frac{l}{2}=\frac{m}{3}=\frac{n}{-1}$
• D. $\frac{l}{2}=\frac{m}{3}=\frac{n}{1}$

Answer 1

The correct option is B 2l+3m-n = 0

If two line segments with direction ratios (a,b,c) and (u,v,w) are perpendicular, then au+bv+cw = 0.

Direction ratios of PQ is given as l,m, n and the line segment has direction ratios 2,3, -1. Since PQ is perpendicular to the given line, $2l+3m-n=0$