1. A small bead is threaded on a smooth, straight horizontal wire which passes through the point \(A ( - 3,1 )\) and the point \(B ( 2,5 )\) in the \(x - y\) plane. The bead moves under the action of a horizontal force \(\mathbf { F }\) of magnitude 8.5 N whose line of action is parallel to the line with equation \(15 x - 8 y + 4 = 0\). The unit on both the \(x\) and \(y\) axes has length one metre. Find the work done by \(\mathbf { F }\) as it moves the bead from \(A\) to \(B\).
   (8)
   
2. A particle \(P\) moves in a plane so that its position vector, \(\mathbf { r }\) metres at time \(t\) seconds, satisfies the differential equation

$$\frac { \mathrm { d } \mathbf { r } } { \mathrm {~d} t } + \mathbf { r } = t \mathbf { i } + \mathrm { e } ^ { - t } \mathbf { j }$$ When \(t = 0\) the particle is at the point with position vector \(( \mathbf { i } + \mathbf { j } ) \mathrm { m }\). Find \(\mathbf { r }\) in terms of \(t\).