Polygon Law of Forces – Definition Check If several forces acting simultaneously on a particle are represented in magnitude and direction by the sides of a polygon taken in order, then the resultant is represented by the closing side of the polygon taken in the opposite direction. Is this statement correct?

Introduction / Context:
Graphical statics often uses the triangle or polygon law for vector addition. The polygon law generalizes the triangle law to more than two forces.

Given Data / Assumptions:

• Concurrent force system acting on a particle.
• Vectors drawn to scale and direction head-to-tail (in order).

Concept / Approach:
The polygon law states that the vector sum of forces equals the closing side from the start to the final head. If the polygon closes, the resultant is zero (equilibrium).

Step-by-Step Solution:
Arrange force vectors head-to-tail in sequence. Draw the closing side from the tail of the first to the head of the last. This closing side equals the resultant in magnitude and direction (opposite if described tail-to-head).

Verification / Alternative check:
Component-wise addition (ΣFx, ΣFy) yields the same resultant as the graphical polygon construction.

Why Other Options Are Wrong:
It applies to any number of forces, not just two or equal forces; it is a planar vector addition rule (and extends to 3D via components).

Common Pitfalls:
Confusing order (head-to-tail) or drawing to inconsistent scales.

Final Answer:
Correct