Ta có $I\in BC$ và 2 IC= 3BI$\Rightarrow 2\overrightarrow{IC}= -3\overrightarrow{IB}$
$\Leftrightarrow 3\overrightarrow{IB} + 2\overrightarrow{IC} = 0$
$\Rightarrow 3\overrightarrow{AB}+ 2\overrightarrow{AC} = 5\overrightarrow{AI}$
$\Leftrightarrow \overrightarrow{AI}=\frac{3}{5}\overrightarrow{AB}+\frac{2}{5}\overrightarrow{AC}$
Có 5JB= 2JC $\overrightarrow{JB}= \frac{2}{5}\overrightarrow{JC}$
$\Leftrightarrow 5\overrightarrow{JB} - 2\overrightarrow{JC} = 0 $
$\Rightarrow 5\overrightarrow{AB} -2\overrightarrow{AC} = 3\overrightarrow{AI}$
$\Leftrightarrow\overrightarrow{AJ} = \frac{5}{3}\overrightarrow{AB} -\frac{2}{3}\overrightarrow{AC}$
Mk đang bận nên lm z thui nhé