#### 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°.

Is there an error in this question or solution?

Solution 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. Concept: Plane - Equation of a Plane in Normal Form.