Vector Algebra

Let $A B C$ be a triangle and $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be the position vectors of $A, B$ and $C$, respectively. Let $D$ divides $B C$ in the ratio $3: 1$ internally and $E$ divides $A D$ in the ratio $4: 1$ internally. Let $B E$ meet $A C$ in $F$. If $E$ divides $B F$ in the ratio $3: 2$ internally, then the position vector of $F$ is