Question

Consider two lines $L_1:\frac{x-7}{3}=\frac{y-7}{2}=\frac{z-3}{1}$ and $L_2:$ $\frac{x-1}{2}=\frac{y+1}{4}=\frac{z+1}{3}$. If a line $L$ whose direction ratios are $⟨2,2,1⟩$ intersect the lines $L_1$ and $L_2$ at $A$ and $B$ then the distance $AB$ is

Answer 1

Answer: 18

$A\equiv 3\lambda +7,2\lambda +7,\lambda +3$
$B=2\mu +1,4\mu -1,3\mu -1$
$\therefore \frac{3\lambda -2\mu +6}{2}=\frac{2\lambda -4\mu +8}{2}$
$=\frac{\lambda -3\mu +4}{1}$

$\therefore \lambda =2$ and $\mu =0$
$\Rightarrow A\equiv (13,11,5),B=(1,-1,-1)$
$\therefore AB=18$