Question

cho \(\Delta\) ABC , M là trung điểm của BC .CMR

\(\overrightarrow{AB}\) + \(\overrightarrow{AC}\) = \(\overrightarrow{AM}\) +\(\overrightarrow{AM}\)

Answer 1

Do M là trung điểm BC \(\Rightarrow\overrightarrow{BM}+\overrightarrow{CM}=\overrightarrow{0}\)

Ta có: \(\overrightarrow{AB}+\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{0}=\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{BM}+\overrightarrow{CM}\)

\(=\left(\overrightarrow{AB}+\overrightarrow{BM}\right)+\left(\overrightarrow{AC}+\overrightarrow{CM}\right)=\overrightarrow{AM}+\overrightarrow{AM}\) (đpcm)