Relative to an origin O, the position vectors of points A and B are given by \(\overrightarrow{OA} = 2\mathbf{i} + 4\mathbf{j} + 4\mathbf{k}\) and \(\overrightarrow{OB} = 3\mathbf{i} + \mathbf{j} + 4\mathbf{k}\).

(i) Use a vector method to find angle \(AOB\).

The point C is such that \(\overrightarrow{AB} = \overrightarrow{BC}\).

(ii) Find the unit vector in the direction of \(\overrightarrow{OC}\).

(iii) Show that triangle OAC is isosceles.