Question

Several forces act on a particle as shown in the figure below (where F1 = 75.0 N, F2 = 65.0 N, θ1 = 25.0° and θ2 = 74.0°, . If the particle is in translational equilibrium, what are the values of F3 (the magnitude of force 3) and θ3 (the angle that force 3 makes with the x axis)?
F1 is 25 degrees West of North
F2 is 74 degrees South of West
F2 is in the direction South of East

Answer 1

F3 is MINUS the vector sum of F1 and F2. I assume you are familiar with the method of adding vectors by adding the x (east) and y (north) components separately.