4. [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.] A line of greatest slope of a fixed smooth plane is parallel to the vector \(( - 4 \mathbf { i } - 3 \mathbf { j } )\). A particle \(P\) falls vertically and strikes the plane. Immediately before the impact, \(P\) has velocity \(- 7 \mathbf { j } \mathrm {~ms} ^ { - 1 }\). Immediately after the impact, \(P\) has velocity \(( - a \mathbf { i } + \mathbf { j } ) \mathrm { ms } ^ { - 1 }\), where \(a\) is a positive constant.

1. Show that \(a = 6\)
2. Find the coefficient of restitution between \(P\) and the plane.