Question

Cho hình bình hành ABCD, M là một điểm trên BC sao cho MB = 3MC. Chứng minh \(\overrightarrow{AM}\)= \(\dfrac{1}{4}\overrightarrow{AB}\) + \(\dfrac{3}{4}\overrightarrow{AC}\)

Answer 1

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

\(=\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{BC}\)

\(=\overrightarrow{AC}+\overrightarrow{CB}+\dfrac{3}{4}\overrightarrow{BC}\)

\(=\overrightarrow{AC}-\dfrac{1}{4}\overrightarrow{BC}\)

\(=\overrightarrow{AB}+\overrightarrow{BC}-\dfrac{1}{4}\overrightarrow{BC}\)

\(=\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{BC}\)

\(=\overrightarrow{AB}+\dfrac{3}{4}\left(\overrightarrow{BA}+\overrightarrow{AC}\right)\)

\(=\dfrac{1}{4}\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{AC}\)