Trong không gian Oxyz cho mặt cầu $\left( S \right) ...

Mặt cầu có tâm $I(0,0,0) R=\sqrt{2}M\in \Delta \Rightarrow M\left( 1,1,t \right)MIM>\sqrt{2}\Leftrightarrow \sqrt{2+{{t}^{2}}}>\sqrt{2}\Leftrightarrow t\ne 0t\in \mathbb{Z}A\left( {{x}_{A}},{{y}_{A}},{{z}_{A}} \right)\left( S \right)\overrightarrow{IA}=\left( {{x}_{A}}, {{y}_{A}},{{z}_{A}} \right){{x}_{A}}\left( x-{{x}_{A}} \right)+{{y}_{A}}\left( y-{{y}_{A}} \right)+{{z}_{A}}\left( z-{{z}_{A}} \right)=0\Leftrightarrow {{x}_{A}}.x+{{y}_{A}}.y+{{z}_{A}}.z-x_{A}^{2}+y_{A}^{2}-{{z}_{A}}^{2}=0\Leftrightarrow {{x}_{A}}.x+{{y}_{A}}.y+{{z}_{A}}z=2M\Rightarrow {{x}_{A}}+{{y}_{A}}+t.{{z}_{A}}=2x+y+t.z-2=0\overrightarrow{{{n}_{1}}}(0,0,1) , \overrightarrow{{{n}_{2}}}=(1,1,t){{30}^{0}}\dfrac{\left| \overrightarrow{{{n}_{1}}}.\overrightarrow{{{n}_{2}}} \right|}{\left| \overrightarrow{{{n}_{1}}} \right|\left| \overrightarrow{{{n}_{2}}} \right|}\le \dfrac{\sqrt{3}}{2}\Leftrightarrow \dfrac{\left| t \right|}{\sqrt{{{t}^{2}}+2}}\le \dfrac{\sqrt{3}}{2}\Leftrightarrow 2\left| t \right|\le \sqrt{3}\sqrt{{{t}^{2}}+2}\Leftrightarrow {{t}^{2}}\le 6\Leftrightarrow \sqrt{6}\le t\le \sqrt{6}t\in \mathbb{Z}t\ne 0t\in \left\{ -2;-1;1;2 \right\}\overrightarrow{IM}=\left( 1;1;t \right)$ làm VTPT.