Angle between two lines

For lines with direction ratios $$a_1, b_1, c_1$$ and $$a_2, b_2, c_2$$:

$$ \cos \theta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}} $$

Perpendicular if $$ a_1 a_2 + b_1 b_2 + c_1 c_2 = 0 $$

Parallel if $$ \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} $$