Cho 2 vectơ \(\overrightarrow{u}\) và \(\overrightarrow{v}\) biết \(\left| \overrightarrow{u} \right|=\sqrt{2};\,\,\,\left| \overrightarrow{v} \right|=3.\)

* Hướng dẫn giải

Do \(\left( \overrightarrow{u},\overrightarrow{v} \right)={{45}^{o}}\Rightarrow \left( 5\overrightarrow{u},-3\overrightarrow{v} \right)={{135}^{o}}.\)

Ta có:

\(\left| \left[ 5\overrightarrow{u},-3\overrightarrow{v} \right] \right|=\left| 5\overrightarrow{u} \right|.\left| -3\overrightarrow{v} \right|.\sin \left( 5\overrightarrow{u},-3\overrightarrow{v} \right)=5\sqrt{2}.9.\sin {{135}^{0}}=45.\)