The points \(P , Q\) and \(R\) have position vectors \(\left( \begin{array} { r } 1 - 2 4 \end{array} \right) , \left( \begin{array} { r } 3 1 - 5 \end{array} \right)\) and \(\left( \begin{array} { l } 2 0 3 \end{array} \right)\) respectively.
Determine a vector equation of the plane that passes through the points \(P , Q\) and \(R\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + \lambda \mathbf { b } + \mu \mathbf { c }\), where \(\lambda\) and \(\mu\) are scalar parameters.
Determine the coordinates of the point of intersection of the plane with the \(x\)-axis.