2. Three forces \(\mathbf { F } _ { 1 } = ( 3 \mathbf { i } - \mathbf { j } + \mathbf { k } ) \mathrm { N } , \mathbf { F } _ { 2 } = ( 2 \mathbf { i } - \mathbf { k } ) \mathrm { N }\), and \(\mathbf { F } _ { 3 }\) act on a rigid body. The force \(\mathbf { F } _ { 1 }\) acts through the point with position vector \(( \mathbf { i } + 2 \mathbf { j } + \mathbf { k } ) \mathrm { m }\), the force \(\mathbf { F } _ { 2 }\) acts through the point with position vector \(( \mathbf { i } - 2 \mathbf { j } ) \mathrm { m }\) and the force \(\mathbf { F } _ { 3 }\) acts through the point with position vector \(( \mathbf { i } + \mathbf { j } + \mathbf { k } ) \mathrm { m }\). Given that the system \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) reduces to a couple \(\mathbf { G }\),

1. find \(\mathbf { G }\). The line of action of \(\mathbf { F } _ { 3 }\) is changed so that the system \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) now reduces to a couple \(( 6 \mathbf { i } + 8 \mathbf { j } + 2 \mathbf { k } ) \mathrm { N }\) m.
2. Find an equation of the new line of action of \(\mathbf { F } _ { 3 }\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + t \mathbf { b }\), where \(\mathbf { a }\) and \(\mathbf { b }\) are constant vectors.