Question

Answer 1

1: ΔABC đều

=>AB=AC=BC=a và \(\hat{BAC}=\hat{ABC}=\hat{ACB}=60^0\)

\(\overrightarrow{AB}\cdot\overrightarrow{AC}\)

\(=AB\cdot AC\cdot cosBAC\)

\(=a\cdot a\cdot cos60=\frac{a^2}{2}\)

2: \(\overrightarrow{AN}=\overrightarrow{AB}+\overrightarrow{BN}\)

\(=\overrightarrow{AB}+\frac13\cdot\overrightarrow{BC}=\overrightarrow{AB}+\frac13\left(\overrightarrow{BA}+\overrightarrow{AC}\right)\)

\(=\overrightarrow{AB}-\frac13\cdot\overrightarrow{AB}+\frac13\cdot\overrightarrow{AC}=\frac23\cdot\overrightarrow{AB}+\frac13\cdot\overrightarrow{AC}\)