dựng hình bình hành $CA'MB'(A'\in AM)$. kẻ $BH,CK\bot AM$
$\overrightarrow{MC}=\overrightarrow{MA'}+\overrightarrow{MB'}(1)$
$\frac{MB'}{MB}=\frac{AC'}{MB}=\frac{A_1C}{A_1B}=\frac{CK}{BH}=\frac{CK.MA}{BH.MA}=\frac{S_{AMC}}{S_{AMB}}$
$=>\overrightarrow{MB'}=\frac{-S_{AMC}}{S_{AMB}}\overrightarrow{MB}(2)$
tương tự $=>\overrightarrow{MA'}=-\frac{S_{MBC}}{S_{ABM}}\overrightarrow{MA}(3)$
$123=>dpcm$