Trying to find the right answer to this..

Three Dimensional Geometry

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

Given points are A (1, 2, 3), B (4, 5, 7), C (– 4, 3, –6) and D (2, 9, 2).
Direction ratios of AB are 4 – 1, 5 – 2, 7 – 3 i.e. 3, 3, 4
Direction ratios of CD are 2 + 4, 9 – 3, 2 + 6 i.e. 6, 6, 8 i.e. 3, 3, 4
Since direction ratios of AB and CD are proportional
∴ AB is parallel to CD.
∴ angle between them is 0°.