Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\overrightarrow u = 2\overrightarrow a - 3\overrightarrow b + \overrightarrow c \\
\Rightarrow \left\{ \begin{array}{l}
{x_{\overrightarrow u }} = 2.{x_{\overrightarrow a }} - 3.{x_{\overrightarrow b }} + {x_{\overrightarrow c }}\\
{y_{\overrightarrow u }} = 2.{y_{\overrightarrow a }} - 3.{y_{\overrightarrow b }} + {y_{\overrightarrow c }}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
{x_{\overrightarrow u }} = 2.2 - 3.3 + 7 = 2\\
{y_{\overrightarrow u }} = 2.1 - 3.4 + 2 = - 8
\end{array} \right.\\
\Rightarrow \overrightarrow u = \left( {2; - 8} \right)\\
b,\\
\overrightarrow x + \overrightarrow a = \overrightarrow b - \overrightarrow c \\
\Rightarrow \overrightarrow x = - \overrightarrow a + \overrightarrow b - \overrightarrow c \\
\Rightarrow \left\{ \begin{array}{l}
{x_{\overrightarrow x }} = - {x_{\overrightarrow a }} + {x_{\overrightarrow b }} - {x_{\overrightarrow c }}\\
{y_{\overrightarrow x }} = - {y_{\overrightarrow a }} + {y_{\overrightarrow b }} - {y_{\overrightarrow c }}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
{x_{\overrightarrow x }} = - 2 + 3 - 7 = - 6\\
{y_{\overrightarrow x }} = - 1 + 4 - 2 = 1
\end{array} \right.\\
\Rightarrow \overrightarrow x = \left( { - 6;1} \right)
\end{array}\)
