a) \(2\overrightarrow a - 4\overrightarrow b + \frac{1}{2}\overrightarrow c = \left( {2.2 - 4.\left( { - 1} \right) + \frac{1}{2}.4;2.0 - 4.\frac{1}{2} + \frac{1}{2}.6} \right) = \left( {10;1} \right)\)
b) \(m\overrightarrow a + \overrightarrow b + n\overrightarrow c = \overrightarrow 0 \Leftrightarrow \left\{ \begin{array}{l}2m - 1 + 4n = 0\\m.0 + \frac{1}{2} + 6n = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}2m + 4n = 1\\6n + \frac{1}{2} = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}n = - \frac{1}{{12}}\\m = \frac{2}{3}\end{array} \right.\)
c) Theo câu b, \(\frac{2}{3}\overrightarrow a + \overrightarrow b - \frac{1}{{12}}\overrightarrow c = \overrightarrow 0 \Leftrightarrow \frac{1}{{12}}\overrightarrow c = \frac{2}{3}\overrightarrow a + \overrightarrow b \Leftrightarrow \overrightarrow c = 8\overrightarrow a + 12\overrightarrow b \)
