The vector from origin to the points $A$ and $B$ are $\overrightarrow{a}=2\hat i-3\hat j-2\hat k$ and $\overrightarrow{b}=2\hat i+3\hat j-\hat k,$ respectively,then the areqa of triangle $OAB$ is

Question

\[(A)\;340\quad(B)\;\sqrt {25}\quad(C)\;\sqrt {229}\quad(D)\;\frac{1}{2}\sqrt {229}\]