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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.
Solution
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, `a_1/a_2=b_1/b_2 = c_1/c_2 = 1/2`
Therefore, AB is parallel to CD.
Thus, the angle between AB and CD is either 0° or 180°.
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