Do I là trung điểm OB \(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{IB}=\frac{1}{2}\overrightarrow{OB}\\\overrightarrow{ID}=\overrightarrow{IO}+\overrightarrow{OD}=\frac{1}{2}\overrightarrow{OD}+\overrightarrow{OD}=\frac{3}{2}\overrightarrow{OD}\end{matrix}\right.\)
\(\Rightarrow\overrightarrow{ID}=-3\overrightarrow{IB}\Rightarrow3\overrightarrow{IB}+\overrightarrow{ID}=\overrightarrow{0}\)
Do đó:
\(3\overrightarrow{AB}+\overrightarrow{AD}=3\left(\overrightarrow{AI}+\overrightarrow{IB}\right)+\overrightarrow{AI}+\overrightarrow{ID}\)
\(=4\overrightarrow{AI}+3\overrightarrow{IB}+\overrightarrow{ID}=4\overrightarrow{AI}\)
