Cho \(\vec a = \left( {2;1} \right),\;\vec b = \le...

B

- Hướng dẫn giải

Lời giải chi tiết:

\(\begin{array}{l}a)\,\,\vec u = 2\vec a - 3\vec b + \vec c = \left( {4;\,2} \right) - \left( {9;12} \right) + \left( {7;2} \right) = \left( {2; - 8} \right)\\b)\,\,\overrightarrow v  + \overrightarrow a  = \overrightarrow b  - \overrightarrow c  \Leftrightarrow \overrightarrow v  =  - \overrightarrow a  + \overrightarrow b  - \overrightarrow c \\ \Leftrightarrow \overrightarrow v  =  - \left( {2;\,\,1} \right) + \left( {3;\,\,4} \right) - \left( {7;\,\,2} \right)\\ \Leftrightarrow \overrightarrow v  = \left( { - 2 + 3 - 7;\,\, - 1 + 4 - 2} \right) = \left( { - 6;\,\,1} \right)\\c)\,\,\overrightarrow c  = k\overrightarrow a  + m\overrightarrow b  = k\left( {2;\,\,1} \right) + m\left( {3;\,\,4} \right)\\ \Leftrightarrow \left( {7;\,\,2} \right) = \left( {2k + 3m;\,\,k + 4m} \right)\\ \Leftrightarrow \left\{ \begin{array}{l}2k + 3m = 7\\k + 4m = 2\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}k = \frac{{22}}{5}\\m =  - \frac{3}{5}\end{array} \right. \Rightarrow \overrightarrow c  = \frac{{22}}{5}\overrightarrow a  - \frac{3}{5}\overrightarrow b .\end{array}\)