Question

Let the foot of the perpendicular of $P(2,-3,1)$ on the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-2}{-1}$ be $Q.$
If direction ratios of the line segment joining P and Q be $l,m,n$, then which of the following relations are correct ?

• 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

$2l+3m-n=0$

Let Q be the foot of the perpendicular P. PQ will be perpendicular to the given line. If two line segments with direction ratios $(a,b,c)\text{and}(u,v,w)$ are perpendicular, then
$au+bv+cw=0$

Direction ratios of PQ is given as $l,m,n$ and the line segment has direction ratios $2,3,-1$

$\Rightarrow 2l+3m-n=0$