What is the cosine of the angle between the lines with direction ratios $2, 2, 1$ and $4, 1, 8$?

Explanation

1. 01

   $\cos \theta = \frac{\lvert a_1a_2 + b_1b_2 + c_1c_2 \rvert}{\sqrt{a_1^{2} + b_1^{2} + c_1^{2}}\sqrt{a_2^{2} + b_2^{2} + c_2^{2}}}$.

2. 02

   $\frac{8 + 2 + 8}{3 \times 9} = \frac{18}{27} = \frac{2}{3}$.