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\includegraphics[max width=\textwidth, alt={}, center]{610c1d96-3833-4a71-a71c-4cac13982332-04_355_533_260_806} A particle \(P\) of mass 8 kg is on a smooth plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. A force of magnitude 100 N , making an angle of \(\theta ^ { \circ }\) with a line of greatest slope and lying in the vertical plane containing the line of greatest slope, acts on \(P\) (see diagram).

1. Given that \(P\) is in equilibrium, show that \(\theta = 66.4\), correct to 1 decimal place, and find the normal reaction between the plane and \(P\).
2. Given instead that \(\theta = 30\), find the acceleration of \(P\).