Applied Mechanics and Graphic Statics
If the given forces P₁, P₂, P₃ and P₄ are such that the force polygon does not close, then the system will

Always reduce to a resultant force
Both (A) and (C)
Always reduce to a couple
Be in equilibrium

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

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