1. A particle moves from the point \(A\) with position vector \(( 3 \mathbf { i } - \mathbf { j } + 3 \mathbf { k } ) \mathrm { m }\) to the point \(B\) with position vector \(( \mathbf { i } - 2 \mathbf { j } - 4 \mathbf { k } ) \mathrm { m }\) under the action of the force \(( 2 \mathbf { i } - 3 \mathbf { j } - \mathbf { k } ) \mathrm { N }\). Find the work done by the force.
   (4)
   
2. A particle \(P\) moves in the \(x - y\) plane so that its position vector \(\mathbf { r }\) metres at time \(t\) seconds satisfies the differential equation

$$\frac { \mathrm { d } ^ { 2 } \mathbf { r } } { \mathrm {~d} t ^ { 2 } } - 4 \mathbf { r } = - 3 \mathrm { e } ^ { t } \mathbf { j }$$ When \(t = 0\), the particle is at the origin and is moving with velocity ( \(2 \mathbf { i } + \mathbf { j }\) ) \(\mathrm { ms } ^ { - 1 }\).
Find \(\mathbf { r }\) in terms of \(t\).