Question

The direction of angle bisector between $\overline{a}$ and $\overline{b}$ can be given by $\frac{\overline{a}+\overline{b}}{2}$

• A. True
• B. False

Answer 1

The correct option is B False

If you construct a parallelogram we get

Using $\overline{a}$ and $\overline{b}$ the diagonal only gives magnitude and directions of resultant. For it to be a bisector both $\overline{a}$ and $\overline{b}$ should be of the same magnitude. So for convenience we will make them unit vectors. i.e., $\frac{\overline{a}}{|a|},\frac{\overline{b}}{|b|},$

Angle bisector of $\overline{a}$ and $\overline{b}$ will lie along $\frac{\overline{a}}{|a|}+\frac{\overline{b}}{|b|}$ and not $\frac{\overline{a}+\overline{b}}{2}$.