for a body to be in equillibrium under the combined action of several forces

...the resultant of all applied forces must be zero at equilibrium

for a body to be in equillibrium, exist two condition:

The sum total of forces in the space vectorial must be zero
sum of forces en x equal zero
sum of forces en y equal zero
sum of forces en z equal zero

and the other condition is:

The sum total of torque in the space vectorial must be zero
sum of torque en x equal zero
sum of torque en y equal zero
sum of torque en z equal zero

enjoy the answer

For a body to be in equilibrium under the combined action of several forces, the net force acting on the body must be zero and the net torque (or moment) acting on the body must also be zero. This means that the forces and torques must balance each other out.

To determine if a body is in equilibrium, you need to consider both the forces and torques acting on the body. Here are the steps to analyze equilibrium:

1. Forces Analysis:
- Identify all the forces acting on the body. These forces can include weight, friction, tension, or any other external forces.
- Resolve each force into its components, typically along x, y, and z axes.
- Sum up all the forces in each direction separately (in x, y, and z axes). The sum of the forces in each direction should be zero (ΣFx = ΣFy = ΣFz = 0) for the body to be in equilibrium.

2. Torques Analysis:
- Identify the point or axis about which the torques are being calculated. This is typically referred to as the pivot point or the axis of rotation.
- Determine the torque produced by each force. Torque is calculated by multiplying the perpendicular distance between the force and the pivot point by the magnitude of the force.
- Add up all the torques (taking into account their direction) acting on the body.
- The sum of all torques should also be zero (Στ = 0) for the body to be in equilibrium.

If both the force and torque conditions are met (ΣFx = ΣFy = ΣFz = 0 and Στ = 0), then the body is in equilibrium under the combined action of several forces. If any of the sum equations are not equal to zero, then the body is not in equilibrium.

It's important to note that this explanation assumes an idealized scenario where the body is rigid and there are no internal or distributed forces acting within the body.