If the coordinates of the points $A,B,C,D$ be $(1,2,3)$ $(4,5,7),( - 4,3, - 6)$ and $(2,9,2)$respectively, then find the angle between the lines AB and CD.

. : Direction ratios of AB are $< 4 - 1,5 - 2,7 - 3 >$
i.e.$< 3,3,4 >$ ...(1).
Direction ratios of CD are $< 2 - ( - 4),9 - 3,2 - ( - 6) >$
i.e. $< 6,6,8 >$ ...(2)

From (1) and (2), Direction ratios of AB and CD are proportional

$\Rightarrow$ The lines AB and CD are parallel.

Hence, the angle between AB and CD is $0^{\circ}$ .