nhầm nha bạn \(0\overrightarrow{AB}+\frac{2}{3}\overrightarrow{AC}=\overrightarrow{AA'}\)

Ta có \(\overrightarrow{A'B}+\overrightarrow{A'C}+\overrightarrow{A'D}=\overrightarrow{0}\)

\(\Leftrightarrow\overrightarrow{AB}-\overrightarrow{AA'}+\overrightarrow{AC}-\overrightarrow{AA'}+\overrightarrow{AD}-\overrightarrow{AA'}=\overrightarrow{0}\)

\(\Leftrightarrow\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}=3\overrightarrow{AA'}\)

\(\Leftrightarrow\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{BC}=3\overrightarrow{AA'}\)

\(\Leftrightarrow\overrightarrow{BA}+\overrightarrow{AC}+\overrightarrow{AB}+\overrightarrow{AC}=3\overrightarrow{AA'}\)

\(\Leftrightarrow0\overrightarrow{AB}+2\overrightarrow{AC}=\overrightarrow{AA'}\)

Vậy \(\overrightarrow{AA'}=0\overrightarrow{AB}+2\overrightarrow{AC}\)