What is the cosine of the acute angle between the lines with direction ratios $3, -6, 2$ and $2, 2, 1$?

Explanation

1. 01

   $3(2) + (-6)(2) + 2(1) = -4$; the lengths are 7 and 3.

2. 02

   For the acute angle, $\cos \theta = \frac{\lvert -4 \rvert}{7 \times 3} = \frac{4}{21}$.