Ta có: ${{d}_{1}}:\left\{ \begin{align} & \overrightarrow{{{u}_{1}}}=\left( -2;3;1 \right) \\ & {{M}_{1}}\left( 1;0;-1 \right)\in {{d}_{1}} \\ \end{align} \right.$,

${{d}_{2}}:\left\{ \begin{align} & \overrightarrow{{{u}_{2}}}=\left( -1;2;-3 \right) \\ & {{M}_{2}}\left( -1;2;7 \right)\in {{d}_{2}} \\ \end{align} \right.$

$\to \left\{ \begin{align} & \left[ \overrightarrow{{{u}_{1}}},\overrightarrow{{{u}_{2}}} \right]=\left( -11;-7;-1 \right) \\ & \overrightarrow{{{M}_{1}}{{M}_{2}}}=\left( -2;2;8 \right) \\ \end{align} \right.\to \left[ \overrightarrow{{{u}_{1}}}.\overrightarrow{{{u}_{2}}} \right].\overrightarrow{{{M}_{1}}{{M}_{2}}}=22-14-8=0$

Suy ra hai đường thẳng trên cắt nhau.