Đáp án:
$\begin{array}{l}
\overrightarrow {AB} = \left( {7; - 3} \right);\overrightarrow {AC} = \left( {3; - 4} \right)\\
1)\overrightarrow {AB} .\overrightarrow {AC} = 7.3 + \left( { - 3} \right).\left( { - 4} \right) = 21 + 12 = 33 \ne 0\\
\Rightarrow A,B,C\,không\,thẳng\,hàng.\\
2)\overrightarrow u = \overrightarrow {AB} - 3\overrightarrow {AC} \\
\Rightarrow \left\{ \begin{array}{l}
x = 7 - 3.3\\
y = - 3 - 3.\left( { - 4} \right)
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = - 2\\
y = 9
\end{array} \right. \Rightarrow \overrightarrow u = \left( { - 2;9} \right)\\
3)D\left( {x;y} \right)\\
\Rightarrow \left\{ \begin{array}{l}
{x_C} = \frac{{{x_A} + {x_B} + {x_D}}}{3}\\
{y_C} = \frac{{{y_A} + {y_B} + {y_D}}}{3}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
1 = \frac{{ - 2 + 5 + x}}{3}\\
- 3 = \frac{{1 - 2 + y}}{3}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 0\\
y = - 8
\end{array} \right.\\
\Rightarrow D\left( {0; - 8} \right)\\
4)ABCE\,là\,hình\,bình\,hành\\
\Rightarrow \overrightarrow {AB} = \overrightarrow {EC} = \left( {7; - 3} \right)\\
\Rightarrow \left\{ \begin{array}{l}
1 - {x_E} = 7\\
- 3 - {y_E} = - 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{x_E} = - 6\\
{y_E} = 0
\end{array} \right. \Rightarrow E\left( { - 6;0} \right)
\end{array}$
