Question

Cho hình thang vuông tại A và D có AD = DC = 6, AB = 3, độ dài \(\left|\overrightarrow{CB}+\overrightarrow{CD}\right|=...\)

Answer 1

Đặt \(\overrightarrow{u}=\overrightarrow{CB}+\overrightarrow{CD}=\overrightarrow{CD}+\overrightarrow{DA}+\overrightarrow{AB}+\overrightarrow{CD}=2\overrightarrow{CD}+\overrightarrow{AB}+\overrightarrow{DA}\)

\(=2\overrightarrow{CD}-\frac{1}{2}\overrightarrow{CD}+\overrightarrow{DA}\) (do \(\overrightarrow{AB}=-\frac{1}{2}\overrightarrow{CD}\))

\(=\frac{3}{2}\overrightarrow{CD}+\overrightarrow{DA}\)

\(\Rightarrow\left|\overrightarrow{u}\right|^2=\frac{9}{4}CD^2+DA^2+3\overrightarrow{CD}.\overrightarrow{DA}=\frac{9}{4}CD^2+DA^2=\frac{13}{4}DA^2\)

\(\Rightarrow\left|\overrightarrow{u}\right|=\frac{\sqrt{13}}{2}DA=3\sqrt{13}\)