\(\overrightarrow{EF}=\overrightarrow{EM}+\overrightarrow{MB}+\overrightarrow{BF}\)
\(\overrightarrow{EM}=\frac{1}{2}\overrightarrow{NM}=\frac{1}{2}\left(\overrightarrow{NA}+\overrightarrow{AM}\right)=\frac{1}{2}\left(-\frac{3}{5}\overrightarrow{AC}+\frac{1}{4}\overrightarrow{AB}\right)=\frac{1}{8}\overrightarrow{AB}-\frac{3}{10}\overrightarrow{AC}\)
\(=\frac{1}{8}\overrightarrow{AB}-\frac{3}{10}\left(\overrightarrow{AB}+\overrightarrow{BC}\right)=-\frac{7}{40}\overrightarrow{AB}-\frac{3}{10}\overrightarrow{BC}\)
\(\overrightarrow{MB}=\frac{3}{4}\overrightarrow{AB}\) ; \(\overrightarrow{BF}=\frac{1}{2}\overrightarrow{BC}\)
\(\Rightarrow\overrightarrow{EF}=\frac{23}{40}\overrightarrow{AB}+\frac{1}{5}\overrightarrow{BC}\)
\(\Rightarrow EF^2=\left(\frac{23}{40}\right)^2AB^2+\frac{1}{25}BC^2+\frac{23}{100}.AB.BC.cos120^0=...\)
Bạn tự thay số, nhìn chán quá :(