Vector Algebra

$\mathbf{a}, \mathbf{b}$ are position vectors of the point $A$ and $B$ respectively, $C$ and $D$ are points on the line $A B$ such that $\mathbf{A B}, \mathbf{A C}$ and $\mathbf{B D}, \mathbf{B A}$ are two pairs of like vectors. If $\mathbf{A C}=3 \mathbf{A B}$ and $\mathbf{B D}=2 \mathbf{B A}$, then $\mathbf{C D}$