9 The lines \(l\) and \(m\) have equations $$\begin{aligned} l : & \mathbf { r } = a \mathbf { i } + 3 \mathbf { j } + b \mathbf { k } + \lambda ( c \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k } )
m : & \mathbf { r } = \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } + \mu ( 2 \mathbf { i } - 3 \mathbf { j } + \mathbf { k } ) \end{aligned}$$ Relative to the origin \(O\), the position vector of the point \(P\) is \(4 \mathbf { i } + 7 \mathbf { j } - 2 \mathbf { k }\).

1. Given that \(l\) is perpendicular to \(m\) and that \(P\) lies on \(l\), find the values of the constants \(a , b\) and \(c\). [4]
2. The perpendicular from \(P\) meets line \(m\) at \(Q\). The point \(R\) lies on \(P Q\) extended, with \(P Q : Q R = 2 : 3\). Find the position vector of \(R\).