A particle \(P\) moves from the point \(A\), with position vector ( \(2 \mathbf { i } + 4 \mathbf { j } + a \mathbf { k }\) ) m , where \(a\) is a positive constant, to the point \(B\), with position vector ( \(- \mathbf { i } + a \mathbf { j } - \mathbf { k }\) ) m , under the action of a constant force \(\mathbf { F } = ( 2 \mathbf { i } + a \mathbf { j } - 3 \mathbf { k } )\) N. The work done by \(\mathbf { F }\), as it moves the particle \(P\) from \(A\) to \(B\), is 3 J . Find the value of \(a\).
(6)