Unit 13.1 Worked Example 2

With respect to the origin $O$ , the position vectors of two points $A$ and $B$  are $\left( 6\mathbf{i}-2\mathbf{j}-\mathbf{k} \right)$ and $\left( -\mathbf{i}+5\mathbf{j}-3\mathbf{k} \right)$ respectively. $C$ is on $AB$ produced such that $2AC=3AB$. Find the position vector of $C$.