The points $O$, $A$ and $B$ are on a plane such that relative to the point $O$, the points $A$ and $B$ have non-parallel position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively. The point $C$ with position vector $\mathbf{c}$ is on the plane $AOB$ such that&nbsp;$OC$ bisects the angle $AOB$. 
Show that&nbsp;$\left(\frac{\mathbf{a}}{|\mathbf{a}|}-\frac{\mathbf{b}}{|\mathbf{b}|}\right)\cdot\mathbf{c}=0$.

The points $O$, $A$ and $B$ are on a plane such that relative to the point $O$, the points $A$ and $B$ have non-parallel position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively. The point $C$ with position vector $\mathbf{c}$ is on the plane $AOB$ such that $OC$ bisects the angle $AOB$.



Show that $\left(\frac{\mathbf{a}}{|\mathbf{a}|}-\frac{\mathbf{b}}{|\mathbf{b}|}\right)\cdot\mathbf{c}=0$.

Vectors - Application of Dot Product: Angle Bisector

Question 02e12f51

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