2.11: Finding an intersection point with two parameters

The diagram shows points $O$, $A$, $B$, $C$, $D$ and $X$. The position vectors of $A$, $B$, and $C$ relative to $O$ are $\overrightarrow{OA} = \mathbf{a}$, $\overrightarrow{OB} = 2\mathbf{b}$ and $\overrightarrow{OC} = 3\mathbf{a}$. The vector $\overrightarrow{CD} = \mathbf{b}$.