Cho 3 vectơ \(\overrightarrow{u}=(3;7;0);\,\,\overrightarrow{v}=(2;3;1);\,\,\overrightarrow{w}=(3;-2;4).\) Biểu thị vectơ \(\overrightarrow{a}=(-4;-12;3)\) theo 3 vectơ \(\overrigh...

* Hướng dẫn giải

Giả sử \(\overrightarrow{a}=m.\overrightarrow{u}+n.\overrightarrow{v}+p.\overrightarrow{w}\Leftrightarrow (-4;-12;3)=(3m;7m;0)+(2n;3n;n)+(3p;-2p;4p)\)

\(\Leftrightarrow \left\{ \begin{array} {} 3m+2n+3p=-4 \\ {} 7m+3n-2p=7 \\ {} n+4p=3 \\ \end{array} \right.\Leftrightarrow \left\{ \begin{array} {} m=-5 \\ {} n=7 \\ {} p=-1 \\ \end{array} \right..\)

Vậy \(\overrightarrow{a}=-5.\overrightarrow{u}+7.\overrightarrow{v}-\overrightarrow{w}.\)