The angle bisector of vectors a and b lies along the direction of their unit vectors' sum or difference. Internal bisector: direction = a/|a| + b/|b| (bisects the angle between them). External bisector: direction = a/|a| - b/|b| (bisects the supplementary angle). This is frequently used in JEE problems asking for the bisector of the angle between two lines or for the incenter of a triangle. Remember: the bisector direction uses UNIT vectors, not the original vectors.