The position vectors of three points \(O, A\) and \(B\) are \(\begin{pmatrix}0\\0\end{pmatrix}, \begin{pmatrix}3\\3.5\end{pmatrix}\) and \(\begin{pmatrix}6\\-1.5\end{pmatrix}\) respectively. Given that \(\mathbf{OD} = \dfrac{1}{3}\mathbf{OB}\) and \(\mathbf{AE} = \dfrac{1}{4}\mathbf{AB}\) write down the position vectors of \(D\) and \(E\).
Given also that \(OE\) and \(AD\) intersect at \(X\), and that \(\mathbf{OX} = p\:\mathbf{OE}\), and that \(\mathbf{XD} = q\:\mathbf{AD}\), find the position vector of \(X\) in terms of (i) \(p\) (ii) \(q\).
Hence calculate \(p\) and \(q\).
