Question

If vectors OA = a and OB = b then show that the vector along the angle bisector of angle AOB is

given by \(\overline{d} = \lambda \left(\frac{\overline{a}}{|\overline{b}|} + \frac{\overline{b}}{|\overline{b}|} \right)\)

Answer 1

Choose any point P on the angle bisector of ∠AOB. Draw PM parallel to OB. 

∴ ∠OPM = ∠POM 

= ∠POB 

Hence, OM = MP

∴ OM and MP is the same scalar multiple of unit vectors \(\hat{a}\) and \(\hat{b}\) along these directions,

Hence, the vector along angle bisector of \(\angle AOB\) is given by