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

$Let \,P=(2λ+1,λ+3,2λ+2)$

$Let\, Q=(μ+2,2μ+2,3μ+3)$

$⇒\frac{12λ−μ−1​}1=\frac{−1λ−2μ+1}{-1}​=\frac{2λ−3μ−1​}{-2}$
$⇒λ=μ=3⇒P(7,6,8) \,\,and ,\,Q(5,8,12)$

$PQ=2\sqrt6$