Question

  

Answer 1

a: \(\overrightarrow{AB}+2\overrightarrow{AC}\)

\(=\overrightarrow{AM}+\overrightarrow{MB}+2\left(\overrightarrow{AM}+\overrightarrow{MC}\right)\)

\(=\overrightarrow{AM}+\overrightarrow{MB}+2\overrightarrow{AM}+2\overrightarrow{MC}\)

\(=3\overrightarrow{AM}+\overrightarrow{MB}+2\overrightarrow{MC}=3\cdot\overrightarrow{AM}\)

b: 

\(\overrightarrow{MA}-\overrightarrow{MG}+\overrightarrow{MB}-\overrightarrow{MG}+\overrightarrow{MC}-\overrightarrow{MG}\)

\(=\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}\)

\(=\overrightarrow{0}\)(do G là trọng tâm của ΔABC)

=>\(\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}=3\cdot\overrightarrow{MG}\)