Question

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.

Answer 1

The coordinates of A,B,C,and D are (1,2,3), (4,5,7), (-4,3,-6), and (2,9,2) respectively.

The direction ratios of AB are (4-1)=3, (5-2)=3, and (7-3)=4
The direction ratios of CD are (2-(-4))=6, (9-3)=6, and (2-(-6))=8

It can be seen that,
$\frac{a^1}{a^2}=\frac{b^1}{b^2}=\frac{c^1}{c^2}= \frac{1}{2}$

Therefore, AB is parallel to CD.

Thus, the angle between AB and CD is either 0° or 180°.