The area of a quadrilateral with diagonals \(\vec{d_1}\) and \(\vec{d_2}\) is \(\frac{1}{2}|\vec{d_1} \times \vec{d_2}|\).

\(\vec{AC} \times \vec{BD} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & 1 \\ -1 & 3 & 2 \end{vmatrix} = \hat{i}(2 - 3) - \hat{j}(4 + 1) + \hat{k}(6 + 1) = -\hat{i} - 5\hat{j} + 7\hat{k}\)

Magnitude = \(\sqrt{1 + 25 + 49} = \sqrt{75} = 5\sqrt{3}\)

Area = \(\frac{5\sqrt{3}}{2}\)

Answer: (A)