a) $\overrightarrow{GA}-2\overrightarrow{GB}+3\overrightarrow{GC}=(\overrightarrow{GA}-\overrightarrow{GB})+(\overrightarrow{GC}-\overrightarrow{GB})+2\overrightarrow{GC}=\overrightarrow{BA}+\overrightarrow{BC}+2\overrightarrow{GC}=\overrightarrow{BD}+2\overrightarrow{GC}=0$
Suy ra G là điểm đối xứng với tâm O qua cạnh CD.
Suy ra: $\overrightarrow{AG}=\overrightarrow{AD}+\overrightarrow{DI}+\overrightarrow{IG}=\frac{3\overrightarrow{AD}}{2}+\frac{\overrightarrow{AB}}{2}$
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