2. $A D 、 B E$ are the medians of $\triangle A B C$ on sides $B C 、 A C$, respectively, and $\overrightarrow{A D}=\vec{a}, \overrightarrow{B E}=\vec{b}$, $\overrightarrow{B C}$ is ( ).
A. $\frac{4}{3} \vec{b}+\frac{2}{3} \vec{a}$
B. $\frac{2}{3} \vec{a}-\frac{2}{3} \vec{b}$
C. $\frac{2}{3} \vec{a}+\frac{2}{3} \vec{b}$
D. $-\frac{2}{3} \vec{a}+\frac{2}{3} \vec{b}$
2. A.

Let $A D$ and $B E$ intersect at point $O$, then $\overrightarrow{B C}=\overrightarrow{B O}+\overrightarrow{O C}=\frac{2}{3} \vec{b}+(\overrightarrow{O D}+\overrightarrow{D C})=\frac{2}{3} \vec{b}+\frac{1}{3} \vec{a}+\frac{1}{2} \overrightarrow{B C}$.