Three Dimensional Geometry Question 7
Question 7 - 25 January - Shift 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
(1) $2 \sqrt{6}$
(2) $3 \sqrt{2}$
(3) $4 \sqrt{3}$
(4) 4
Show Answer
Answer: (1)
Solution:
Formula: Direction Cosines And Direction Ratio
Let $P=(2 \lambda+1, \lambda+3,2 \lambda+2)$
Let $Q=(\mu+2,2 \mu+2,3 \mu+3)$
$\Rightarrow \frac{2 \lambda-\mu-1}{1}=\frac{\lambda-2 \mu+1}{-1}=\frac{2 \lambda-3 \mu-1}{-2}$
$\Rightarrow \lambda=\mu=3 \Rightarrow P(7,6,8)$ and $Q(5,8,12)$
$PQ=2 \sqrt{6}$
