C

- Hướng dẫn giải

Ta gọi \(A\left( a,\,b \right)\), \(B\left( -b,\,a \right)\), \(C\left( a-b,\,a+b \right)\) nên \(\overrightarrow{AB}\left( -b-a,\,a-b \right)\), \(\overrightarrow{AC}\left( -b,\,a \right)\)

\(S=\frac{1}{2}\left| \left[ \overrightarrow{AB},\overrightarrow{AC} \right] \right|\) \(=\frac{1}{2}\left| -{{a}^{2}}-{{b}^{2}} \right|\)\(\Leftrightarrow \frac{1}{2}\left( {{a}^{2}}+{{b}^{2}} \right)=18\)\(\Leftrightarrow \sqrt{{{a}^{2}}+{{b}^{2}}}=6\)