6
\includegraphics[max width=\textwidth, alt={}, center]{d0fa61eb-f320-427e-8883-de224d293933-4_474_831_269_657} Forces of magnitudes \(P \mathrm {~N}\) and 25 N act at right angles to each other. The resultant of the two forces has magnitude \(R \mathrm {~N}\) and makes an angle of \(\theta ^ { \circ }\) with the \(x\)-axis (see diagram). The force of magnitude \(P \mathrm {~N}\) has components - 2.8 N and 9.6 N in the \(x\)-direction and the \(y\)-direction respectively, and makes an angle of \(\alpha ^ { \circ }\) with the negative \(x\)-axis.

1. Find the values of \(P\) and \(R\).
2. Find the value of \(\alpha\), and hence find the components of the force of magnitude 25 N in
   (a) the \(x\)-direction,
   (b) the \(y\)-direction.
3. Find the value of \(\theta\).