$\begin{array}{l}A(-2;3)\quad B(1;-4)\quad C(5;-1)\\ \to \begin{cases}\overrightarrow{AB} = (3;-7)\\\overrightarrow{BC} = (4;3)\\\overrightarrow{OB} =(1;-4)\\\overrightarrow{OC} = (5;-1) \end{cases}\\ a) \quad Gọi\,\,\overrightarrow{u}=(a,b)\\ \quad \overrightarrow{u}= \overrightarrow{AB} - 7\overrightarrow{BC}\\ \Leftrightarrow \begin{cases}a = 3 - 7.4 = -25\\b = -7 -7.3 = -28 \end{cases}\\ Vậy\,\,\overrightarrow{u} = (-25;-28) b)\quad \overrightarrow{u} = (-4;3)\\ \quad \overrightarrow{u} = m\overrightarrow{AB} + n\overrightarrow{BC}\\ \Leftrightarrow \begin{cases}-4 = 3m +4n\\3 = -7m +3n \end{cases}\\ \Leftrightarrow \begin{cases}m = -\dfrac{24}{37}\\n =-\dfrac{19}{37}\end{cases} \\c)\quad Gọi\,\,D(x;y)\\ \Rightarrow \overrightarrow{CD} = (x-5;y+1)\\ \text{Khi đó:}\,\,\overrightarrow{CD} =3\overrightarrow{OB} - 2\overrightarrow{BC} + \overrightarrow{OC}\\ \Leftrightarrow \begin{cases}x - 5 = 3.1 -2.4 +5\\y + 1 =3.(-7) -2.3 + (-1) \end{cases}\\ \Leftrightarrow \begin{cases} x = 5\\y = -29\end{cases}\\ Vậy\,\,D(5;-29) \end{array}$
