4. A force system consists of three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) acting on a rigid body.
\(\mathbf { F } _ { 1 } = ( \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }\) and acts at the point with position vector \(( - \mathbf { i } + 4 \mathbf { j } ) \mathrm { m }\).
\(\mathbf { F } _ { 2 } = ( - \mathbf { j } + \mathbf { k } ) \mathrm { N }\) and acts at the point with position vector ( \(\left. 2 \mathbf { i } + \mathbf { j } + \mathbf { k } \right) \mathrm { m }\).
\(\mathbf { F } _ { 3 } = ( 3 \mathbf { i } - \mathbf { j } + \mathbf { k } ) \mathrm { N }\) and acts at the point with position vector \(( \mathbf { i } - \mathbf { j } + 2 \mathbf { k } ) \mathrm { m }\).
It is given that this system can be reduced to a single force \(\mathbf { R }\).

1. Find \(\mathbf { R }\).
   (2)
2. Find a vector equation of the line of action of \(\mathbf { R }\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + \lambda \mathbf { b }\), where \(\mathbf { a }\) and \(\mathbf { b }\) are constant vectors and \(\lambda\) is a parameter.
   (10)