Đáp án:
\(\overrightarrow {AB} = \frac{{25}}{{19}}\overrightarrow {BC} - \frac{{18}}{{19}}\overrightarrow {DC} .\)
Giải thích các bước giải:
\(\begin{array}{l}
B\left( { - 2;\,\,1} \right),\,\,\,C\left( {3;\,\,4} \right),\,\,\,D\left( { - 5;\,\,3} \right)\\
\Rightarrow \overrightarrow {BC} = \left( {5;\,\,3} \right);\,\,\overrightarrow {DC} = \left( {8;\,\,1} \right)\\
f)\,\,\,A\left( { - 1; - 2} \right)\\
\overrightarrow {AB} = \left( { - 1;\,\,3} \right)\\
Goi\,\,m,\,\,n\,\,\,la\,\,\,cac\,\,so\,\,thuc\,\,thoa\,\,man\,\,\,\overrightarrow {AB} = m\overrightarrow {BC} + n\overrightarrow {DC} \\
\Rightarrow \left( { - 1;\,\,\,3} \right) = m\left( {5;\,\,3} \right) + n\left( {8;\,\,1} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
- 1 = 5m + 8n\\
3 = 3m + n
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m = \frac{{25}}{{19}}\\
n = - \frac{{18}}{{19}}
\end{array} \right.\\
\Rightarrow \overrightarrow {AB} = \frac{{25}}{{19}}\overrightarrow {BC} - \frac{{18}}{{19}}\overrightarrow {DC} .
\end{array}\)
