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\includegraphics[max width=\textwidth, alt={}, center]{41b1f65b-8806-4183-81a1-0276691e203c-04_598_696_255_246}
\includegraphics[max width=\textwidth, alt={}, center]{41b1f65b-8806-4183-81a1-0276691e203c-04_465_67_294_1023} A rigid lamina of negligible mass is in the form of a rhombus ABCD , where \(\mathrm { AC } = 6 \mathrm {~m}\) and \(\mathrm { BD } = 8 \mathrm {~m}\). Forces of magnitude \(2 \mathrm {~N} , 4 \mathrm {~N} , 3 \mathrm {~N}\) and 5 N act along its sides \(\mathrm { AB } , \mathrm { BC } , \mathrm { CD }\) and DA , respectively, as shown in the diagram. A further force \(\mathbf { F }\) N, acting at A, and a couple of magnitude \(G N m\) are also applied to the lamina so that it is in equilibrium.

1. Determine the magnitude and direction of \(\mathbf { F }\).
2. Determine the value of \(G\).