A particle is subjected to two forces, F1 and F2. F1 has a magnitude of 10 N and acts at 30^ counter-clockwise from the positive x-axis. F2 has a magnitude of 15 N and acts at 70^ with the negative y-

To solve this problem, we need to resolve each force into its horizontal (x) and vertical (y) components, find the resultant force, and then determine the magnitude and direction of the force required to achieve equilibrium.

The angles for the forces, measured counter-clockwise from the positive x-axis, are:

• For $F_1 = 10 \, \text{N}$: $\theta_1 = 30^\circ$.
• For $F_2 = 15 \, \text{N}$: The angle is $70^\circ$ with the negative y-axis. This means $\theta_2 = 90^\circ + (90^\circ - 70^\circ) =