Relative to an origin \(O\), the position vectors of the points \(A\) and \(B\) are \(2\mathbf i+12\mathbf j\) and \(6\mathbf i-4\mathbf j\) respectively.

(i) Write down and simplify an expression for \(\overrightarrow{AB}\).

The point \(C\) lies on \(\overrightarrow{AB}\) such that \(AC:CB\) is \(1:3\).

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

The point \(D\) lies on \(\overrightarrow{OA}\) such that \(OD:DA\) is \(1:3\).

(iii) Find an expression for \(\overrightarrow{AD}\) in terms of \(\mathbf i\) and \(\mathbf j\).