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

\(\overrightarrow{OA} = \begin{pmatrix} 0 \\ 2 \\ -3 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 2 \\ 5 \\ -2 \end{pmatrix} \quad \text{and} \quad \overrightarrow{OC} = \begin{pmatrix} 3 \\ p \\ q \end{pmatrix}.\)

(i) In the case where \(ABC\) is a straight line, find the values of \(p\) and \(q\).

(ii) In the case where angle \(BAC\) is \(90^\circ\), express \(q\) in terms of \(p\).

(iii) In the case where \(p = 3\) and the lengths of \(AB\) and \(AC\) are equal, find the possible values of \(q\).