The points $O$, $A$ and $B$ are on a plane such that relative to the point $O$, the points \

Question

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

Accepted Answer

$\left(\dfrac{\mathbf a}{\lvert\mathbf a\rvert}-\dfrac{\mathbf b}{\lvert\mathbf b\rvert}\right)\cdot\mathbf c=0$

Vectors - Angle Bisectors Using Vectors

Vectors - Angle Bisectors Using Vectors

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