question_answer 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:

direction ratios of line AB are 4 ?1, 5 ? 2, 7 ? 3, i.e. 3, 3, 4       Also, direction ratios of line CD are 2 + 4, 9 ? 3, 2 + 6 i.e. 6, 6, 8.       As       line AB and CD are parallel. Hence angle between line AB and CD is 0°.