Trong không gian với hệ trục tọa độ $Oxyz$, cho mặt phẳng $\left(...

Ta có $\left( S \right):\left\{ \begin{matrix}
I\left( 1;1;-2 \right) \\
R=3 \\
\end{matrix} \right.$$\Rightarrow d\left( I,\left( P \right) \right)=5\overrightarrow{MN}\overrightarrow{u}=\left( 0;1;-1 \right)\sin \left( MN,\left( P \right) \right)=\dfrac{\left| \overrightarrow{u}.\overrightarrow{n}_{\left( P \right)} \right|}{\left| \overrightarrow{u} \right|\left| \overrightarrow{n}_{\left( P \right)} \right|}=\dfrac{1}{\sqrt{2}}N'N\left( P \right)NMN'N'\Rightarrow MN=\dfrac{NN'}{\sin \left( MN,\left( P \right) \right)}MNNN'N{{{N}'}_{\min }}=\text{d}\left( I,\left( P \right) \right)-R=2\Rightarrow M{{N}_{\min }}=2\sqrt{2}IN'NNI{N}'$.