If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (

1.	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» Dr’s of AB = (3, 3, 4), Direction CD = (6,6, 8) \(\frac{3}{6} = \frac{3}{6} = \frac{4}{8}\) Dr’s are proportional. Hence they are parallel ∴ Angle between them = 0°

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»

Dr’s of AB = (3, 3, 4),

Direction CD = (6,6, 8)

\(\frac{3}{6} = \frac{3}{6} = \frac{4}{8}\)

Dr’s are proportional.

Hence they are parallel

∴ Angle between them = 0°