What is the cosine of the angle between the line through $A(1, 3, -2)$ and $B(3, 1, -1)$ and the line through $C(-1, 0, 2)$ and $D(5, 2, 5)$?

Explanation

1. 01

   Direction ratios: $AB$ gives $2, -2, 1$ (length 3) and $CD$ gives $6, 2, 3$ (length 7).

2. 02

   $\cos \theta = \frac{\lvert 12 - 4 + 3 \rvert}{3 \times 7} = \frac{11}{21}$.