Em tự vẽ hình nhé.
\(\begin{array}{l}
+ )\,\,3\overrightarrow {FA} + 2\overrightarrow {FC} = \overrightarrow 0 \Leftrightarrow 3\overrightarrow {FA} + 2\overrightarrow {FA} + 2\overrightarrow {AC} = \overrightarrow 0 \\
\Leftrightarrow 5\overrightarrow {FA} = - 2\overrightarrow {AC} \Leftrightarrow \overrightarrow {AF} = \dfrac{2}{5}\overrightarrow {AC} \\
+ )\,\,\overrightarrow {EA} = 2\overrightarrow {EB} \Leftrightarrow \overrightarrow {EA} = 2\overrightarrow {EA} + 2\overrightarrow {AB} \Leftrightarrow \overrightarrow {AE} = 2\overrightarrow {AB} \\
Ta\,co:\\
\overrightarrow {EF} = \overrightarrow {EA} + \overrightarrow {AF} = - 2\overrightarrow {AB} + \dfrac{2}{5}\overrightarrow {AC} = - \dfrac{2}{5}\left( {5\overrightarrow {AB} - \overrightarrow {AC} } \right)\\
Goi\,\,M\,\,la\,trung\,diem\,\,BC.\\
\Rightarrow \overrightarrow {AG} = \dfrac{2}{3}\overrightarrow {AM} = \frac{2}{3}.\frac{1}{2}\left( {\overrightarrow {AB} + \overrightarrow {AC} } \right) = \frac{1}{3}\overrightarrow {AB} + \dfrac{1}{3}\overrightarrow {AC} \\
Do\,do:\,\overrightarrow {EG} = \overrightarrow {EA} + \overrightarrow {AG} = - 2\overrightarrow {AB} + \dfrac{1}{3}\overrightarrow {AB} + \dfrac{1}{3}\overrightarrow {AC} \\
= - \dfrac{5}{3}\overrightarrow {AB} + \dfrac{1}{3}\overrightarrow {AC} = - \dfrac{1}{3}\left( {5\overrightarrow {AB} - \overrightarrow {AC} } \right)\\
Suy\,\,ra:\,\overrightarrow {EF} = \dfrac{6}{5}\overrightarrow {EG} \,\,hay\,\,\overline {E,F,\,G}
\end{array}\)
