Question

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 $P Q$ is

• A. $3 \sqrt{2}$
• B. 4
• C. $2 \sqrt{6}$
• D. $4 \sqrt{3}$

Answer 1

Answer: (C)

$2 \sqrt{6}$

Answer 2

The correct answer is (C) : $2\sqrt6$
Let P = (2λ+1,λ+3,2λ+2)
Let Q = $(\mu+2,2\mu+2,3\mu+3)$
$⇒\frac{2λ-\mu-1}{1}=\frac{λ-2\mu-1}{-1}$
$=\frac{2λ-3\mu-1}{-2}⇒λ=\mu=3$
$⇒P(7,6,8)$ and $Q(5,8,12)$
PQ = $2\sqrt6$