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 1

The direction ratios of AB and CD are proportional to 3, 3, 4 and 6, 6, 8, respectively.

Let $\theta$ be the angle between AB and CD. Then,

$$\begin{gathered} \cos \theta =\frac{3\times 6+3\times 6+4\times 8}{\sqrt{3^2+3^2+4^2}\sqrt{6^2+6^2+8^2}} \\ =\frac{68}{\sqrt{34}\sqrt{136}} \\ =1 \\ \Rightarrow \theta =0° \end{gathered}$$