What is the angle between the lines $\frac{x - 1}{1} = \frac{y + 1}{2} = \frac{z}{2}$ and $\frac{x + 2}{2} = \frac{y - 3}{-2} = \frac{z - 1}{1}$?

Explanation

1. 01

   Direction ratios $1, 2, 2$ and $2, -2, 1$: $1(2) + 2(-2) + 2(1) = 0$.

2. 02

   $\cos \theta = 0$, so the lines are perpendicular: $\frac{\pi}{2}$.