1.9: Triangle with an internal intersection point

The diagram shows the triangle $OAC$. The point $B$ is the midpoint of $OC$. The point $Y$ lies on $AC$ such that $OY$ intersects $AB$ at the point $X$ where $AX:XB = 3:1$. It is given that $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$.