JEE Main 2023 (Online) 25th January Morning ShiftQuestion 1
Consider the lines $L_1$ and $L_2$ given by
$L_1:\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2}$
$L_2:\frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$
A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is
3D Geometry
Solution
$P=(1+2p,3+p,2+2p)$, $Q=(2+q,2+2q,3+3q)$, $\vec{PQ}\parallel(1,-1,-2)$ gives $q=p=3$, $\vec{PQ}=-2(1,-1,-2)$. $PQ=2\sqrt6$.