For lines with direction vectors $b_{1}$ and $b_{2}$: cos(theta) = |$b_{1}$.$b_{2}$|/(|$b_{1}$||$b_{2}$|). The absolute value ensures the acute angle (0 ≤ theta ≤ pi/2). Lines are perpendicular when $b_{1}$.$b_{2}$ = 0 (i.e., a_{1}$$a_{2}+b_{1}$$b_{2}+c_{1}$$c_{2} = 0). Lines are parallel when $b_{1}$ = k**$b_{2}$** for some scalar k (i.e., $a_{1}$/$a_{2}$ = $b_{1}$/$b_{2}$ = $c_{1}$/$c_{2}$). Note: in 3D, non-parallel non-intersecting lines are called skew lines.