lf $A, B, C, D$are points $(2, 3, -1), (3,5, - 3), (1, 2, 3), ( 3, 5, 7)$ respectively, then the angle between AB and CD, is

 

Direction ratios of AB and CD are proportional to

$3-2,5-3,-3+1$ and $3-1,5-2,7-3$

or $1, 2,-2$ and $2, 3, 4$

respectively.

Let $\theta$ be the angle between AB and CD. Then, 

$\cos \theta =\frac{1\times 2+2\times 3+(-2)\times 4}{\sqrt{1+4+4}}=0\Rightarrow \theta =\frac{\pi }{2}$