Applied Mechanics and Graphic Statics
If a set of given forces are such that their free vectors build a closed polygon, then

The resultant force is zero but resultant couple may not be zero
The resultant force and resultant couple are always zero
The resultant force and resultant couple both may not be zero
The resultant force is zero but resultant couple is not zero

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Applied Mechanics and Graphic Statics
A point subjected to a number of forces will be in equilibrium, if

Sum of resolved parts in any two directions at right angles, are both zero
Algebraic sum of the moments of the forces about the point is zero
Algebraic sum of the forces is zero
Two resolved parts in any two directions at right angles are equal

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