(i) The vector \(\overrightarrow{MO}\) is expressed as \(4\mathbf{i} - 6\mathbf{k}\).

The vector \(\overrightarrow{MC}\) is expressed as \(4\mathbf{i} + 4\mathbf{j} + 6\mathbf{k}\).

(ii) To find the angle \(\angle OMC\), we use the dot product formula:

\(\overrightarrow{MO} \cdot \overrightarrow{MC} = 4 \times 4 + 0 \times 4 + (-6) \times 6 = 16 - 36 = -20\).

The magnitudes are \(|\overrightarrow{MO}| = \sqrt{4^2 + 6^2} = \sqrt{52}\) and \(|\overrightarrow{MC}| = \sqrt{4^2 + 4^2 + 6^2} = \sqrt{68}\).

Using the cosine formula: \(\overrightarrow{MO} \cdot \overrightarrow{MC} = |\overrightarrow{MO}| |\overrightarrow{MC}| \cos \theta\).

\(-20 = \sqrt{52} \times \sqrt{68} \times \cos \theta\).

\(\cos \theta = \frac{-20}{\sqrt{52} \times \sqrt{68}}\).

\(\theta = \cos^{-1}\left(\frac{-20}{\sqrt{52} \times \sqrt{68}}\right) \approx 109.7^\circ\).