What is the angle between the lines $\frac{x + 1}{3} = \frac{4 - y}{2} = \frac{z}{6}$ and $\frac{x - 2}{2} = \frac{y + 3}{6} = \frac{z - 1}{3}$?

Explanation

1. 01

   $\frac{4 - y}{2} = \frac{y - 4}{-2}$, so the first line has direction ratios $3, -2, 6$ and the second $2, 6, 3$; both have length 7.

2. 02

   $\cos \theta = \frac{\lvert 6 - 12 + 18 \rvert}{7 \times 7} = \frac{12}{49}$, so $\theta = \cos^{-1}\frac{12}{49}$.