Chọn: Đáp án B

$\overrightarrow{a}=\left( 3;-2;1 \right),\overrightarrow{b}=\left( 2;1;-1 \right)\Rightarrow \overrightarrow{u}=m\overrightarrow{a}-3\overrightarrow{b}=\left( 3m-6;-2m-3;m+3 \right)$

$\overrightarrow{v}=3\overrightarrow{a}-2m\overrightarrow{b}=\left( 9-4m;-6-2m;3+2m \right)$

$\overrightarrow{u}$ cùng phương$\overrightarrow{v}\Leftrightarrow \frac{3m-6}{9-4m}=\frac{-2m-3}{-6-2m}=\frac{m+3}{3+2m}$

$\Leftrightarrow \left\{ \begin{align}  & \left( 3m-6 \right)\left( 6+2m \right)=\left( 9-4m \right)\left( 2m+3 \right) \\  & {{\left( 2m+3 \right)}^{2}}=\left( m+3 \right)\left( 6+2m \right) \\ \end{align} \right.\Leftrightarrow {{m}^{2}}=\frac{9}{2}\Leftrightarrow m=\pm \frac{3\sqrt{2}}{2}$