(a) Find the unit vector in the direction of \(5\mathbf{i}-15\mathbf{j}\).

(b) The position vectors of points \(A\) and \(B\) relative to an origin \(O\) are \(\begin{pmatrix}3\\-5\end{pmatrix}\) and \(\begin{pmatrix}12\\7\end{pmatrix}\) respectively. The point \(C\) lies on \(AB\) such that \(AC:CB=2:1\).

(i) Find the position vector of \(C\) relative to \(O\).

The point \(D\) lies on \(OB\) such that \(OD:OB=1:\lambda\) and \(\overrightarrow{DC}=\begin{pmatrix}6\\1.25\end{pmatrix}\).

(ii) Find the value of \(\lambda\).