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

\(\overrightarrow{OA} = \begin{pmatrix} 3 \\ 0 \\ -4 \end{pmatrix}\) and \(\overrightarrow{OB} = \begin{pmatrix} 6 \\ -3 \\ 2 \end{pmatrix}\).

(i) Find the cosine of angle \(AOB\).

The position vector of \(C\) is given by \(\overrightarrow{OC} = \begin{pmatrix} k \\ -2k \\ 2k - 3 \end{pmatrix}\).

(ii) Given that \(AB\) and \(OC\) have the same length, find the possible values of \(k\).