Ta có :
V_{S.ABCD}=\frac{1}{3}.SH.S_{ABCD} =\frac{1}{3}.SH.(S_{ABD}+S_{BCD})
\Leftrightarrow \frac{27}{2}=\frac{1}{3}.SH.(3\sqrt{3}+6\sqrt{3})
\Leftrightarrow SH=3\sqrt{3}(*)
Lại có : SH vuông góc (ABCD)\Rightarrow \overrightarrow{SH}=k.\overrightarrow{n_{ABCD}}
\Rightarrow (x,y-1,z-5)=k.(1;1;1)\Rightarrow S(k,k+1;k+5)
Thế vào (*)\Rightarrow k=\pm 3\Rightarrow S(...)