Đáp án:
\[\overrightarrow u = \left( {0;\,\,1} \right)\]
Giải thích các bước giải:
\[\begin{array}{l}
AB:\,\,\,2x - 3y + 3 = 0\\
CD:\,\,2x - 3y - 6 = 0\\
b)\,\,\overrightarrow u = \left( {x;\,\,y} \right) \bot \overrightarrow {AB} ;\,\,\,\,CD = {T_{\overrightarrow u }}\left( {AB} \right)\\
\overrightarrow {AB} = \left( {3;\,\,2} \right)\\
\overrightarrow u \bot \overrightarrow {AB} \Rightarrow \overrightarrow u .\overrightarrow {AB} = 0 \Leftrightarrow 3x + 2y = 0\,\,\,\,\left( 1 \right)\\
Goi\,\,\,M\left( {0\,;\,\,1} \right) \in AB;\,\,\,M'\left( {x';\,\,y'} \right)\,\,\,la\,\,\,anh\,\,\,cua\,\,\,M\,\,\,qua\,\,\,{T_{\overrightarrow u }}\\
\Rightarrow \left\{ \begin{array}{l}
x' = x\\
y' = y + 1
\end{array} \right.\\
M' \in CD \Rightarrow 2x' - 3y' - 6 = 0\\
\Leftrightarrow 2x - 3y - 3 - 6 = 0\\
\Leftrightarrow 2x - 3y = 9\,\,\,\,\left( 2 \right)\\
Tu\,\,\,\left( 1 \right)\,\,\,va\,\,\,\left( 2 \right)\,\,\,ta\,\,\,co\,\,hpt\,\,\,\left\{ \begin{array}{l}
3x + 2y = 0\\
2x - 3y = 9
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 0\\
y = 1
\end{array} \right.\\
\Rightarrow \overrightarrow u = \left( {0;\,\,1} \right).
\end{array}\]
