Question

cho tứ giác ABCD , xác định các điểm M , N , P sao cho

a , \(2\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}=\overrightarrow{0}\)

Answer 1

Gọi G là trọng tâm tam giác ABC

\(2\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}=\overrightarrow{0}\)

\(\Leftrightarrow2\left(\overrightarrow{MG}+\overrightarrow{GA}\right)+\overrightarrow{MG}+\overrightarrow{GB}+\overrightarrow{MG}+\overrightarrow{GC}=\overrightarrow{0}\)

\(\Leftrightarrow4\overrightarrow{MG}+\overrightarrow{GA}+\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}=\overrightarrow{0}\)

\(\Leftrightarrow4\overrightarrow{MG}+\overrightarrow{GA}=\overrightarrow{0}\)

\(\Leftrightarrow\overrightarrow{MG}=\frac{1}{4}\overrightarrow{AG}\)