回復 3# P78961118 的帖子
易知\(\overline{AB}=\sqrt{7},\overline{AC}=2\sqrt{3},\overline{BC}=\sqrt{13}\)
定座標\(A\left( 0,0,0 \right),O\left( 0,2,0 \right),C\left( 2\sqrt{3},0,0 \right),B\left( x,y,z \right)\)
\(\begin{align}
& {{x}^{2}}+{{y}^{2}}+{{z}^{2}}=7 \\
& {{x}^{2}}+{{\left( y-2 \right)}^{2}}+{{z}^{2}}=9 \\
& {{\left( x-2\sqrt{3} \right)}^{2}}+{{y}^{2}}+{{z}^{2}}=13 \\
& x=\frac{\sqrt{3}}{2},y=\frac{1}{2},z=\sqrt{6} \\
& O-ABC=2\sqrt{3}\times 2\times \frac{1}{2}\times \sqrt{6}\times \frac{1}{3}=2\sqrt{2} \\
\end{align}\)
