What is the sine of the angle between the lines with direction ratios $1, -2, 2$ and $4, 0, 3$?

Explanation

1. 01

   $\cos \theta = \frac{\lvert 4 + 0 + 6 \rvert}{3 \times 5} = \frac{2}{3}$.

2. 02

   $\sin \theta = \sqrt{1 - \frac{4}{9}} = \frac{\sqrt{5}}{3}$.