Relative to the origin \(O\), the points \(A\), \(B\), and \(C\) have position vectors given by

\(\overrightarrow{OA} = \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 4 \\ 3 \\ 2 \end{pmatrix}, \quad \text{and} \quad \overrightarrow{OC} = \begin{pmatrix} 3 \\ -2 \\ -4 \end{pmatrix}.\)

The quadrilateral \(ABCD\) is a parallelogram.

(a) Find the position vector of \(D\).

(b) The angle between \(BA\) and \(BC\) is \(\theta\). Find the exact value of \(\cos \theta\).

(c) Hence find the area of \(ABCD\), giving your answer in the form \(p\sqrt{q}\), where \(p\) and \(q\) are integers.