6 Relative to the origin \(O\), the points \(A , B\) and \(C\) have position vectors given by
$$\overrightarrow { O A } = \left( \begin{array} { l }
2
1
3
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { l }
4
3
2
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r }
3
- 2
- 4
\end{array} \right) .$$
The quadrilateral \(A B C D\) is a parallelogram.
- Find the position vector of \(D\).
- The angle between \(B A\) and \(B C\) is \(\theta\).
Find the exact value of \(\cos \theta\).
- Hence find the area of \(A B C D\), giving your answer in the form \(p \sqrt { q }\), where \(p\) and \(q\) are integers.