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

Ta có \)">\left( S \right)I\left( -1;1;0 \right)R=2IA=\sqrt{4+1+16}=\sqrt{21}>R\Rightarrow A\left( S \right)IB=\sqrt{1+1+1}=\sqrt{3}<R\Rightarrow B\left( S \right)H,KI\left( P \right)ABIH\le IKIK\left( P \right)\left( S \right)\Leftrightarrow IH\Leftrightarrow H\equiv K\overrightarrow{IK}\left( P \right)\overrightarrow{AB}=\left( 1;2;3 \right)AB\left\{ \begin{aligned}
& x=t \\
& y=2t \\
& z=1+3t \\
\end{aligned} \right.K\left( t;2t;1+3t \right)\in AB\overrightarrow{IK}=\left( t+1;2t-1;1+3t \right)\overrightarrow{IK}\bot \overrightarrow{AB}\Leftrightarrow t+1+2\left( 2t-1 \right)+3\left( 1+3t \right)=0\Leftrightarrow 14t=-2\Leftrightarrow t=-\dfrac{1}{7}\Rightarrow \overrightarrow{IK}=\left( \dfrac{6}{7};-\dfrac{9}{7};\dfrac{4}{7} \right)\overrightarrow{{{n}_{P}}}=\left( 6;-9;4 \right)\left( P \right)6x-9y+4z-4=0\Leftrightarrow -\dfrac{9}{2}x+\dfrac{27}{4}y-3z+3=0a+b+c=-\dfrac{3}{4}$.