\(\overrightarrow{AB}=\left(-3;-3;8\right)\)
\(\overrightarrow{AC}=\left(-2;0;6\right)\)
\(\overrightarrow{BC}=\left(1;3;-2\right)\)
\(\Rightarrow S_{\Delta ABC}=\dfrac{1}{2}\left|\left[\overrightarrow{AB};\overrightarrow{AC}\right]\right|=\sqrt{91}\)
\(BC=\sqrt{1^2+3^2+\left(-2\right)^2}=\sqrt{14}\)
\(\Rightarrow AH^2=\left(\dfrac{2S_{\Delta ABC}}{BC}\right)^2=26\)



