Cho 3 vectơ \(\overrightarrow{u}=(1;x;-1);\,\,\,\overrightarrow{v}=(0;2;1);\,\,\,\overrightarrow{w}=(x;7;2).\) Tìm x biết rằng \(\left[ \overrightarrow{u},\overrightarrow{v} \right...

* Hướng dẫn giải

\(\left[ \overrightarrow{u},\overrightarrow{v} \right]=(x+2;-1;2) \\\Rightarrow \left[ \overrightarrow{u},\overrightarrow{v} \right].\overrightarrow{w}={{x}^{2}}+2x-7+4=0 \\\Leftrightarrow {{x}^{2}}+2x-3=0 \\\Leftrightarrow \left[ \begin{array} {} x=1 \\ {} x=-3 \\ \end{array} \right..\)