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} = kb_{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.