a) Ta có: \(\overrightarrow u = 3\overrightarrow a + 2\overrightarrow b - 4\overrightarrow c \)\( = \left( {3.2 + 2.3 - 4.( - 7);3.1 + 2.( - 4) - 4.2} \right)\) \( = \left( {40; - 13} \right)\)
Vậy \(\overrightarrow u = (40; - 13)\)
b) Ta có: \(\overrightarrow x + \overrightarrow a = \overrightarrow b - \overrightarrow c \)\( \Leftrightarrow \overrightarrow x = \overrightarrow b - \overrightarrow c - \overrightarrow a \)\( = \left( {3 - \left( { - 7} \right) - 2; - 4 - 2 - 1} \right)\)\( = \left( {8; - 7} \right)\)
c) Ta có: \(k\overrightarrow a + h\overrightarrow b = (2k + 3h;k - 4h)\)
\(\overrightarrow c = k\overrightarrow a + h\overrightarrow b \)\( \Leftrightarrow \left\{ \begin{array}{l}2k + 3h = - 7\\k - 4h = 2\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}k = - 2\\h = - 1\end{array} \right.\)
