If θ is the angle between the vectors    a→ and b→ , then the unit vector along the angular bisector of  a→ and b→  will be given by

Vector in the direction of angular bisector of   a→ and b→ is a→+b→2Unit vector in this direction is a→+b→|a→+b→|From the figure, position vector of E is a→+b→2 Now in triangle AEB,AE=ABcos⁡θ2⇒a→+b→2=cos⁡θ2Hence, unit vector along the bisector is a→+b→2cos⁡(θ/2)