13. Given that $\overrightarrow{A C}$ is the sum vector of $\overrightarrow{B A}$ and $\overrightarrow{B D}$, and $\overrightarrow{B D}$ is the sum vector of $\overrightarrow{A D}$ and $\frac{2}{3} \overrightarrow{A B}$. If $\overrightarrow{A C}=\vec{a}, \overrightarrow{B D}=\vec{b}$, try to express $\overrightarrow{A B}+\overrightarrow{A D}$ in terms of $\vec{a}$ and $\vec{b}$.
13. $\left\{\begin{array}{l}\overrightarrow{A C}=\overrightarrow{B A}+\overrightarrow{B D} \\ \overrightarrow{B D}=\overrightarrow{A D}+\frac{2}{3} \overrightarrow{A B},\end{array}\right.$ we get $\left\{\begin{array}{l}\overrightarrow{A B}=\vec{b}-\vec{a} \\ \overrightarrow{A D}=\frac{2}{3} \vec{a}+\frac{1}{3} \vec{b},\end{array}\right.$ thus $\overrightarrow{A B}+\overrightarrow{A D}=\frac{4}{3} \vec{b}-\frac{1}{3} \vec{a}$.