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Đặt \(\overrightarrow{u}=\overrightarrow{CD}+2\overrightarrow{CB}=\overrightarrow{CD}+2\left(\overrightarrow{CD}+\overrightarrow{DA}+\overrightarrow{AB}\right)\)
\(=3\overrightarrow{CD}+2\overrightarrow{DA}-\overrightarrow{CD}\) (do \(2\overrightarrow{AB}=\overrightarrow{DC}=-\overrightarrow{CD}\))
\(=2\overrightarrow{CD}+2\overrightarrow{DA}=2\overrightarrow{CA}\)
\(\Rightarrow\left|\overrightarrow{u}\right|=2AC=2\sqrt{AD^2+CD^2}=4\sqrt{5}\)
Đặt \(\overrightarrow{u}=\overrightarrow{AB}+\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{DC}=3.\overrightarrow{AB}+\overrightarrow{AD}\) (do \(\overrightarrow{DC}=2\overrightarrow{AB}\))
\(\Rightarrow\left|\overrightarrow{u}\right|^2=\left(3\overrightarrow{AB}+\overrightarrow{AD}\right)^2=9AB^2+AD^2+6\overrightarrow{AB}.\overrightarrow{AD}=9AB^2+AD^2=10AB^2\)
\(\Rightarrow\left|\overrightarrow{u}\right|=AB\sqrt{10}=2\sqrt{10}\)
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 \(\overrightarrow{AB}=-\frac{1}{2}\overrightarrow{CD}\))
\(=\frac{3}{2}\overrightarrow{CD}+\overrightarrow{DA}\)
\(\Rightarrow\left|\overrightarrow{u}\right|^2=\frac{9}{4}CD^2+DA^2+3\overrightarrow{CD}.\overrightarrow{DA}=\frac{9}{4}CD^2+DA^2=\frac{13}{4}DA^2\)
\(\Rightarrow\left|\overrightarrow{u}\right|=\frac{\sqrt{13}}{2}DA=3\sqrt{13}\)