The points $A$ and $B$ have position vectors $4\mathbf{i}+3\mathbf{k}$ and \(8\mathbf{i}-6\mat

Question

The points $A$ and $B$ have position vectors $4\mathbf{i}+3\mathbf{k}$ and $8\mathbf{i}-6\mathbf{k}$ respectively. The point $C$ on the line segment $AB$ is such that $(1-k)AC=kBC$. By using the scalar product, find the value of $k$ such that $OC$ bisects the angle $AOB$.

Accepted Answer

$k=\dfrac13$

Vectors - Angle Bisectors Using Vectors

Vectors - Angle Bisectors Using Vectors

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