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\(\overrightarrow{BN}=\overrightarrow{BA}+\overrightarrow{AN}=-\overrightarrow{AB}+\frac{1}{3}\overrightarrow{AC}\)
\(\overrightarrow{BM}=\overrightarrow{BA}+\overrightarrow{AM}=-\overrightarrow{AB}+\frac{1}{2}\overrightarrow{AD}=-\overrightarrow{AB}+\frac{1}{2}\left(\frac{1}{2}\overrightarrow{AB}+\frac{1}{2}\overrightarrow{AC}\right)\)
\(\overrightarrow{BM}=-\frac{3}{4}\overrightarrow{AB}+\frac{1}{4}\overrightarrow{AC}=\frac{3}{4}\left(-\overrightarrow{AB}+\frac{1}{3}\overrightarrow{AC}\right)=\frac{3}{4}\overrightarrow{BN}\)
\(\Rightarrow B;M;N\) thẳng hàng
\(\overrightarrow{BM}=\dfrac{\overrightarrow{BA}+\overrightarrow{BC}}{2}=\dfrac{\overrightarrow{BA}+\overrightarrow{BA}+\overrightarrow{AC}}{2}=-\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{AC}\)
\(\overrightarrow{AN}=\overrightarrow{AB}+\overrightarrow{BN}=\overrightarrow{AB}+\dfrac{2}{5}\overrightarrow{BA}+\dfrac{2}{5}\overrightarrow{AC}=\dfrac{3}{5}\overrightarrow{AB}+\dfrac{2}{5}\overrightarrow{AC}\)
Câu 1:
\(\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}\)
\(=\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{BC}\)
\(=\overrightarrow{AB}+\dfrac{2}{3}\left(\overrightarrow{BA}+\overrightarrow{AC}\right)\)
\(=\dfrac{1}{3}\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{AC}\)
