1 A particle rests on a smooth, horizontal plane. Horizontal unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) lie in this plane. The particle is in equilibrium under the action of the three forces \(( - 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { N }\) and \(( 21 \mathbf { i } - 7 \mathbf { j } ) \mathrm { N }\) and \(\mathbf { R N }\).

1. Write down an expression for \(\mathbf { R }\) in terms of \(\mathbf { i }\) and \(\mathbf { j }\).
2. Find the magnitude of \(\mathbf { R }\) and the angle between \(\mathbf { R }\) and the \(\mathbf { i }\) direction.