3 The vertices of a triangular lamina, which is in the \(x - y\) plane, are at the origin O and the points \(A ( 2,3 )\) and \(B ( - 2,1 )\). Forces \(2 \mathbf { i } + \mathbf { j }\) and \(- 3 \mathbf { i } + 2 \mathbf { j }\) are applied to the lamina at A and B , respectively, and a force \(\mathbf { F }\), whose line of action is in the \(x - y\) plane, is applied at O . The three forces form a couple.

1. Determine the magnitude and the direction of \(\mathbf { F }\).
2. Determine the magnitude and direction of the additional couple that must be applied to the lamina in order to keep it in equilibrium.