A small bead is threaded on a smooth straight horizontal wire. The wire is modelled as a line with vector equation \(\mathbf { r } = ( 2 + \lambda ) \mathbf { i } + ( 2 \lambda - 1 ) \mathbf { j }\), where the unit of length is the metre. The bead is moved a distance of \(\sqrt { 80 } \mathrm {~m}\) along the wire by a force \(\mathbf { F } = ( 4 \mathbf { i } - 3 \mathbf { j } ) \mathrm { N }\). Find the magnitude of the work done by \(\mathbf { F }\).
(5)