在△ABC中\( \overrightarrow{AB}=c,\overrightarrow{AC}=b,\)若点D.满足\( \overrightarrow{BD}\)=2\( \overrightarrow{DC},\)则\( \overrightarrow{AD}\)= ( )
A. \( \frac{2}{3}b＋\frac{1}{3}c\)
B. \( \frac{5}{3}c-\frac{2}{3}b\) C. \( \frac{2}{3}b-\frac{1}{3}c\)
