2
\includegraphics[max width=\textwidth, alt={}, center]{f4f2996b-5382-4b0d-9804-b5f5945946b3-2_636_519_664_813} Three horizontal forces of magnitudes \(F \mathrm {~N} , 63 \mathrm {~N}\) and 25 N act at \(O\), the origin of the \(x\)-axis and \(y\)-axis. The forces are in equilibrium. The force of magnitude \(F \mathrm {~N}\) makes an angle \(\theta\) anticlockwise with the positive \(x\)-axis. The force of magnitude 63 N acts along the negative \(y\)-axis. The force of magnitude 25 N acts at \(\tan ^ { - 1 } 0.75\) clockwise from the negative \(x\)-axis (see diagram). Find the value of \(F\) and the value of \(\tan \theta\).