\(\begin{array}{l}
\text{Ta có:}\\
\quad NC = 2NA\\
\Rightarrow \overrightarrow{CN} = \dfrac23\overrightarrow{CA}\\
\text{Ta được:}\\
\quad \overrightarrow{BN} = \overrightarrow{BC} + \overrightarrow{CN}\\
\Leftrightarrow \overrightarrow{BN} =\overrightarrow{BC} + \dfrac23\overrightarrow{CA}\\
\Leftrightarrow \overrightarrow{BN} =\overrightarrow{BC}+ \dfrac23\left(\overrightarrow{BA} - \overrightarrow{BC}\right)\\
\Leftrightarrow \overrightarrow{BN} =\dfrac13\overrightarrow{BC} + \dfrac23\overrightarrow{BA}
\end{array}\)
