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)

b: \(m=sinx+cosx=\sqrt{2}\cdot sin\left(x+\dfrac{\Omega}{4}\right)\)

=>\(\left|m\right|=\sqrt{2}\cdot\left|sin\left(x+\dfrac{\Omega}{4}\right)\right|\)

\(0< =\left|sin\left(x+\dfrac{\Omega}{4}\right)\right|< =1\)

=>\(0< =\sqrt{2}\cdot\left|sin\left(x+\dfrac{\Omega}{4}\right)\right|< =\sqrt{2}\)

=>\(\left|m\right|< =\sqrt{2}\)

Ta có: \(2sinx.cosx=m^2-1\)

\(\left|\left(sinx-cosx\right)\right|=\sqrt{sin^2x-2sinxcosx+cos^2x}\)

\(=\sqrt{1-\left(m^2-1\right)}=\sqrt{2-m^2}\)

\(\Leftrightarrow2-m^2\ge0\)

\(\Leftrightarrow m^2\le2\)

\(\Leftrightarrow\left|m\right|\le\sqrt{2}\)