If 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

$\frac{\pi}{2}$

Direction 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{1×2+2 ×3 + (-2) × 4}{\sqrt{1+4+4}\sqrt{4+5+16}}= 0 ⇒ \theta = \frac{\pi}{2}$