(i) Resolve the forces horizontally and vertically:

Horizontal component: \(X = 75 + 50 \cos 60^\circ = 100\)

Vertical component: \(Y = 50 \sin 60^\circ = 43.3\)

Resultant force: \(\sqrt{100^2 + 43.3^2} = 109 \text{ N}\)

Direction: \(\text{Angle} = \arctan\left(\frac{43.3}{100}\right) = 23.4^\circ\) anticlockwise from the positive x-axis.

(ii) For equilibrium, resolve forces:

Horizontal: \(50 \cos \alpha - F \cos 50^\circ = 0\)

Vertical: \(50 \sin \alpha - 3F - F \sin 50^\circ = 0\)

\(\tan \alpha = \frac{3F + F \sin 50^\circ}{F \cos 50^\circ}\)

Solving gives \(\alpha = 80.3^\circ\) and \(F = 13.1 \text{ N}\).