What we know for certain is that the resultant force would also be in the same plane. However, its direction depends upon the directions of the forces in the group. If all the forces happen to be parallel, then the resultant force would also be parallel to these forces; otherwise, we have to rely on vector algebra to determine its exact direction.

The direction of the moment vector would be perpendicular to the plane in which the forces are located.

This principle says that the moment produced by a force about a point is equal to the sum of moments about the same point produced by the components of the force.

No. The summation of forces being zero is merely a necessary but not a sufficient condition for equilibrium of a rigid body. To have equilibrium, the summation of moments about an arbitrary point must also be equal to zero.

If a member is loaded by only three concentrated forces, it is referred to as a three-force member. To maintain equilibrium, the three forces would have to be either parallel or concurrent, and not all be in the same direction.

What we can do in this case is to find the position vector from the moment center to any point along the line of action of the force. Then we can find the desired moment by the cross product of the position vector and the force vector.

A rigid body is said to be in the state of equilibrium when the sum of forces and the sum of moments acting on it are zero. Mathematically, we can express the equilibrium of a rigid body under a general three-dimensional loading system as

or in vector form as

The important thing to realize is that a body can never be in the state of equilibrium with only a single force or a single moment acting on it.

Yes you can, but you must be careful that the resultant is in the same direction as the distributed force and it is placed at the centroid of the distributed area.

We use free-body diagrams to first identify the known as well as unknown forces and moments acting on a body. Then with the help of equilibrium equations we solve for the unknown forces and moments.