\(\overrightarrow{BN}=\overrightarrow{BA}+\overrightarrow{AN}=-\overrightarrow{AB}+\frac{1}{3}\overrightarrow{AC}\)
\(\overrightarrow{BM}=\overrightarrow{BA}+\overrightarrow{AM}=-\overrightarrow{AB}+\frac{1}{2}\overrightarrow{AD}=-\overrightarrow{AB}+\frac{1}{2}\left(\frac{1}{2}\overrightarrow{AB}+\frac{1}{2}\overrightarrow{AC}\right)\)
\(\overrightarrow{BM}=-\frac{3}{4}\overrightarrow{AB}+\frac{1}{4}\overrightarrow{AC}=\frac{3}{4}\left(-\overrightarrow{AB}+\frac{1}{3}\overrightarrow{AC}\right)=\frac{3}{4}\overrightarrow{BN}\)
\(\Rightarrow B;M;N\) thẳng hàng