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Coplanar forces of magnitudes \(50 \mathrm {~N} , 40 \mathrm {~N}\) and 30 N act at a point \(O\) in the directions shown in the diagram, where \(\tan \alpha = \frac { 7 } { 24 }\).
- Find the magnitude and direction of the resultant of the three forces.
- The force of magnitude 50 N is replaced by a force of magnitude \(P \mathrm {~N}\) acting in the same direction. The resultant of the three forces now acts in the positive \(x\)-direction. Find the value of \(P\).