(i) To find \(\overrightarrow{DA}\), we calculate:

\(\overrightarrow{DA} = \overrightarrow{OA} - \overrightarrow{OD} = (8\mathbf{i}) - (2\mathbf{i} + 4\mathbf{k}) = 6\mathbf{i} - 4\mathbf{k}\).

To find \(\overrightarrow{CA}\), we calculate:

\(\overrightarrow{CA} = \overrightarrow{OA} - \overrightarrow{OC} = (8\mathbf{i}) - (2\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}) = 6\mathbf{i} - 5\mathbf{j} - 4\mathbf{k}\).

(ii) To find angle \(CAD\), use the scalar product:

\(\overrightarrow{CA} \cdot \overrightarrow{DA} = (6\mathbf{i} - 5\mathbf{j} - 4\mathbf{k}) \cdot (6\mathbf{i} - 4\mathbf{k}) = 36 + 16 = 52\).

Calculate the magnitudes:

\(|\overrightarrow{DA}| = \sqrt{6^2 + 0^2 + (-4)^2} = \sqrt{52}\).

\(|\overrightarrow{CA}| = \sqrt{6^2 + (-5)^2 + (-4)^2} = \sqrt{77}\).

Using the cosine formula:

\(52 = \sqrt{77} \cdot \sqrt{52} \cdot \cos \angle CAD\).

\(\cos \angle CAD = \frac{52}{\sqrt{77} \cdot \sqrt{52}} \approx 0.82178\).

\(\angle CAD \approx 34.7^\circ\) or \(0.606 \text{ radians}\).