Từ giả thiết ta có: $\left\{ \begin{align} & \left( P \right)\bot \left( Q \right) \\ & d\left( M;\left( Q \right) \right)=\sqrt{2} \\ \end{align} \right.$$\Leftrightarrow \left\{ \begin{align} & A+B+C=0 \\ & \frac{\left| A+2B-C \right|}{\sqrt{{{A}^{2}}+{{B}^{2}}+{{C}^{2}}}}=\sqrt{2} \\ \end{align} \right.$

$\left\{ \begin{align} & A=-B-C \\ & \frac{\left| B-2C \right|}{\sqrt{2{{B}^{2}}+2{{C}^{2}}+2BC}}=\sqrt{2}\left( * \right) \\ \end{align} \right.$

$\left( * \right)\Leftrightarrow B=0$hoặc  $3B+8C=0$