a:
\(\overrightarrow{CA}=\left(3-x;0-y\right)\)
=>\(\overrightarrow{CA}=\left(3-x;-y\right)\)
\(\overrightarrow{CB}=\left(-3-x;0-y\right)\)
=>\(\overrightarrow{CB}=\left(-x-3;-y\right)\)
\(\overrightarrow{CA}+3\overrightarrow{CB}=\overrightarrow{0}\)
=>\(\overrightarrow{CA}=-3\overrightarrow{CB}\)
=>\(\left\{{}\begin{matrix}3-x=-3\left(-3-x\right)\\0-y=-3\left(0-y\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3-x+3\left(-3-x\right)=0\\-y+3\cdot\left(-y\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3-x-9-3x=0\\y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{3}{2}\\y=0\end{matrix}\right.\)
=>C(-1,5;0)
b: \(\overrightarrow{DA}=\left(3-x;0-y\right)\)
=>\(\overrightarrow{DA}=\left(3-x;-y\right)\)
\(\overrightarrow{DB}=\left(-3-x;0-y\right)\)
=>\(\overrightarrow{DB}=\left(-3-x;-y\right)\)
\(\overrightarrow{DA}-3\overrightarrow{DB}=\overrightarrow{0}\)
=>\(\overrightarrow{DA}=3\overrightarrow{DB}\)
=>\(\left\{{}\begin{matrix}3-x=3\left(-3-x\right)\\-y=3\left(-y\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3-x+3\left(x+3\right)=0\\y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12+2x=0\\y=0\end{matrix}\right.\)
=>x=-6 và y=0
=>D(-6;0)
