Đáp án:
a) \(\left( {2; - 8} \right)\)
b) \(\left( { - 6;1} \right)\)
c) \(\left\{ \begin{array}{l}
k = \dfrac{{22}}{5}\\
l = - \dfrac{3}{5}
\end{array} \right.\)
d) \(m = \dfrac{3}{{16}}\)
Giải thích các bước giải:
$\begin{array}{l}
\overrightarrow a = \left( {2;1} \right),\overrightarrow b = \left( {3;4} \right),\overrightarrow c = \left( {7;2} \right)\\
a)\,\overrightarrow u = 2\overrightarrow a - 3\overrightarrow b + \overrightarrow c \\
= \left( {2.2 - 3.3 + 7;2.1 - 3.4 + 2} \right) = \left( {2; - 8} \right)\\
b)\,\overrightarrow x + \overrightarrow a = \overrightarrow b - \overrightarrow c \\
\Leftrightarrow \overrightarrow x = \overrightarrow b - \overrightarrow c - \overrightarrow a = \left( {3 - 7 - 2;4 - 2 - 1} \right) = \left( { - 6;1} \right)\\
c)\,\overrightarrow c = k\overrightarrow a + l\overrightarrow b \Leftrightarrow \left\{ \begin{array}{l}
7 = 2k + 3l\\
2 = k + 4l
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
k = \dfrac{{22}}{5}\\
l = - \dfrac{3}{5}
\end{array} \right.\\
d)\,\overrightarrow d \,cung\,phuong\,\overrightarrow c \left( {7;2} \right)\\
\Leftrightarrow \dfrac{{m + 2}}{7} = \dfrac{{1 - 2m}}{2} \Leftrightarrow 2m + 4 = 7 - 14m\\
\Leftrightarrow 16m = 3 \Leftrightarrow m = \dfrac{3}{{16}}
\end{array}$
