Question

Cho hình vuông ABCD tâm O cạnh a, độ dài \(\left|\overrightarrow{AB}+\overrightarrow{2AD}\right|\) là...

Answer 1

Đặt \(\overrightarrow{u}=\overrightarrow{AB}+2\overrightarrow{AD}\Rightarrow\left|\overrightarrow{u}\right|^2=\left(\overrightarrow{AB}+2\overrightarrow{AD}\right)^2\)

\(\Leftrightarrow\left|\overrightarrow{u}\right|^2=AB^2+4AD^2+4\overrightarrow{AB}.\overrightarrow{AD}=AB^2+4AD^2=5a^2\)

\(\Rightarrow\left|\overrightarrow{u}\right|=a\sqrt{5}\) hay \(\left|\overrightarrow{AB}+2\overrightarrow{AD}\right|=a\sqrt{5}\)