Đáp án:
$\overrightarrow{MN} = -\dfrac23\overrightarrow{a} + \dfrac13\overrightarrow{b}$
Giải thích các bước giải:
$\begin{array}{l}\overrightarrow{MN} = \overrightarrow{MA} + \overrightarrow{AN}\\ = \overrightarrow{MB} - \overrightarrow{AB} + \overrightarrow{AN}\\ = \dfrac13\overrightarrow{CB} - \overrightarrow{AB} + \dfrac{2}{3}\overrightarrow{AC}\\ = \dfrac13(\overrightarrow{CA} + \overrightarrow{AB}) - \overrightarrow{AB} + \dfrac{2}{3}\overrightarrow{AC}\\ = \left(\dfrac13\overrightarrow{AB} - \overrightarrow{AB}\right) + \left(\dfrac23\overrightarrow{AC} - \dfrac13\overrightarrow{AC}\right)\\ = - \dfrac23\overrightarrow{AB} + \dfrac13\overrightarrow{AC}\\= -\dfrac23\overrightarrow{a} + \dfrac13\overrightarrow{b}\end{array}$
