Gọi O là tâm hình bình hành \(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{BG}=\frac{2}{3}\overrightarrow{BO}\\\overrightarrow{BO}=\frac{1}{2}\overrightarrow{BD}\end{matrix}\right.\) \(\Rightarrow\overrightarrow{BG}=\frac{1}{3}\overrightarrow{BD}\)
\(\overrightarrow{NG}=\frac{1}{3}\overrightarrow{NC}\) (theo t/c trọng tâm)
\(\overrightarrow{BA}=2\overrightarrow{BN}=2\left(\overrightarrow{BG}+\overrightarrow{GN}\right)\)
\(\Rightarrow\overrightarrow{GA}=\overrightarrow{GB}+\overrightarrow{BA}=\overrightarrow{GB}+2\overrightarrow{BG}+2\overrightarrow{GN}=\overrightarrow{BG}+2\overrightarrow{GN}\)
\(\Rightarrow\overrightarrow{GA}=\overrightarrow{BG}-2\overrightarrow{NG}=\frac{1}{3}\overrightarrow{BD}-\frac{2}{3}\overrightarrow{NC}\)