(i) When the force is parallel to the plane, resolve the forces parallel to the plane. The component of the weight down the plane is \(18 \sin 30^{\circ}\). For equilibrium, this must equal the force \(P\), so:

\(P = 18 \cos 60^{\circ}\)

\(P = 9\)

(ii) When the force is horizontal, resolve the forces perpendicular to the plane. The horizontal force \(P\) has a component \(P \cos 30^{\circ}\) parallel to the plane. For equilibrium, this must balance the component of the weight down the plane:

\(P \cos 30^{\circ} = 18 \cos 60^{\circ}\)

\(P = \frac{18 \cos 60^{\circ}}{\cos 30^{\circ}}\)

\(P = 10.4\)