Bài 5:
\(\overrightarrow{AB}-\overrightarrow{AD}=\overrightarrow{DA}+\overrightarrow{AB}=\overrightarrow{DB}\)
\(\overrightarrow{AE}-\overrightarrow{AC}=\overrightarrow{CA}+\overrightarrow{AE}=\overrightarrow{CE}\)
Vì \(\overrightarrow{BD}=\overrightarrow{EC}\)
nên \(\overrightarrow{DB}=\overrightarrow{CE}\)
=>\(\overrightarrow{AB}-\overrightarrow{AD}=\overrightarrow{AE}-\overrightarrow{AC}\)
=>\(\overrightarrow{AB}+\overrightarrow{AC}=\overrightarrow{AE}+\overrightarrow{AD}\)
Bài 6:
Vì I là trung điểm của MN
nên \(\overrightarrow{IM}+\overrightarrow{IN}=\overrightarrow{0}\)
\(\overrightarrow{IA}+\overrightarrow{IB}-\overrightarrow{CI}-\overrightarrow{DI}\)
\(=\overrightarrow{IA}+\overrightarrow{ID}+\overrightarrow{IB}+\overrightarrow{IC}\)
\(=2\left(\overrightarrow{IM}+\overrightarrow{IN}\right)=2\overrightarrow{0}=\overrightarrow{0}\)
=>\(\overrightarrow{IA}+\overrightarrow{IB}=\overrightarrow{CI}+\overrightarrow{DI}\)
