\(\overrightarrow{MB}.\overrightarrow{MN}=\left(\overrightarrow{AB}-\overrightarrow{AM}\right)\left(\overrightarrow{CN}-\overrightarrow{CM}\right)\)\(=\left(\overrightarrow{AB}-\dfrac{1}{4}\overrightarrow{AC}\right)\left(-\dfrac{1}{2}\overrightarrow{DC}+\dfrac{3}{4}\overrightarrow{AC}\right)\)\(=\left[\overrightarrow{AB}-\dfrac{1}{4}\left(\overrightarrow{AD}+\overrightarrow{AB}\right)\right]\left[-\dfrac{1}{2}\overrightarrow{AB}+\dfrac{3}{4}\left(\overrightarrow{AD}+\overrightarrow{AB}\right)\right]\)
\(=\left(\dfrac{3}{4}\overrightarrow{AB}-\dfrac{1}{4}\overrightarrow{AD}\right)\left(\dfrac{1}{4}\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{AD}\right)\)
\(=\dfrac{3}{16}AB^2+\dfrac{9}{16}\overrightarrow{AB}.\overrightarrow{AD}-\dfrac{1}{16}\overrightarrow{AB}.\overrightarrow{AD}-\dfrac{3}{16}AD^2\)
\(=\dfrac{3}{16}AB^2+0-0-\dfrac{3}{16}AB^2=0\)
Bạn tham khảo nha. Chúc bạn học tốt!
