5. 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.

Answers (1)

Direction ratios of  AB are (4-1),(5-2),(7-3) = 3,3,4

and Direction ratios of CD are (2-(-4)), (9-3), (2-(-6)) = 6,6,8

So, it can be noticed 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, we can easily say the angle between AB and CD which is either 0^{\circ}\ or\ 180^{\circ}.

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