Question

If a line with direction ratio $2: 1: 1$ intersects the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{ x -2}{1}=\frac{ y +1}{2}=\frac{ z +2}{3}$ at $A$ and $B$ then $|\overrightarrow{ AB }|$ is

• A. $2 \sqrt{3}$
• B. $2 \sqrt{5}$
• C. $2 \sqrt{6}$
• D. $2 \sqrt{7}$

Answer 1

Answer: (C)

$ A =(2 \alpha+1,3 \alpha+2,4 \alpha+3)$
$B =(\beta+2,2 \beta-1,3 \beta-2)$

Solving (I) & (II) $\Rightarrow 4 \alpha-3 \beta+7=0$
Solving (II) & (III) $\Rightarrow \alpha-\beta+2=0$
$\alpha=-1, \beta=1, A (-1,-1,-1) ; B (3,1,1)$
$AB =2 \sqrt{6}$