a: \(\overrightarrow{NC}=-2\cdot\overrightarrow{NA}\)
=>NC=2NA và N nằm giữa A và C
AC=AN+NC
=AN+2AN
=3AN
\(\overrightarrow{BN}=\overrightarrow{BA}+\overrightarrow{AN}\)
\(=\overrightarrow{BA}+\frac13\cdot\overrightarrow{AC}\)
\(=\overrightarrow{BA}+\frac13\left(\overrightarrow{AB}+\overrightarrow{BC}\right)=\frac23\cdot\overrightarrow{BA}+\frac13\cdot\overrightarrow{BC}=\frac13\left(2\cdot\overrightarrow{BA}+\overrightarrow{BC}\right)\)
b: \(\overrightarrow{BE}=\overrightarrow{BC}+\overrightarrow{CE}\)
\(=\overrightarrow{BC}+2\cdot\overrightarrow{CD}=\overrightarrow{BC}+2\cdot\overrightarrow{BA}\)
\(=3\cdot\overrightarrow{BN}\)
=>B,N,E thẳng hàng
