Giải thích các bước giải:
Ta có:
$\overrightarrow a = \left( {3;2} \right),\overrightarrow b = \left( {1; - 2} \right),\overrightarrow c = \left( {0;5} \right)$
a) Ta có:
$\begin{array}{l}
\overrightarrow x = 2\overrightarrow a - \overrightarrow b - \overrightarrow c \\
\Leftrightarrow \overrightarrow x = \left( {2.3 - 1 - 0;2.2 - \left( { - 2} \right) - 5} \right)\\
\Leftrightarrow \overrightarrow x = \left( {5;1} \right)
\end{array}$
Vậy $\overrightarrow x = \left( {5;1} \right)$
b) Ta có:
$\begin{array}{l}
\overrightarrow c = m\overrightarrow a + n\overrightarrow b \\
\Leftrightarrow \left\{ \begin{array}{l}
0 = m.3 + n.1\\
5 = m.2 + n.\left( { - 2} \right)
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m = \dfrac{5}{8}\\
n = \dfrac{{ - 15}}{8}
\end{array} \right.
\end{array}$
Vậy $\overrightarrow c = \dfrac{5}{8}\overrightarrow a - \dfrac{{15}}{8}\overrightarrow b $
