Law of Polygon of Forces — choose the correct statement that defines the polygon method for the resultant and equilibrium of coplanar concurrent forces.

Introduction / Context:
The polygon law generalizes the parallelogram law to more than two concurrent forces. It provides a graphical method to determine the single resultant of several forces acting at a point, and to check equilibrium when the force polygon closes.

Given Data / Assumptions:

• Forces are coplanar and concurrent.
• A consistent scale is used to represent magnitudes.
• Vectors are drawn head-to-tail in sequence.

Concept / Approach:

Arrange force vectors one after another, preserving magnitude and direction. The straight line joining the start of the first vector to the end of the last vector (the “closing side”) represents the single resultant. If the polygon closes (end meets start), the resultant is zero and the system is in equilibrium.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Component-wise vector addition of all forces yields the same resultant as the closing side in the graphical construction.

Why Other Options Are Wrong:

(a) describes the special equilibrium case only, not the general resultant construction. (c) contains distorted wording; while “opposite order” appears in some texts, option (b) states the standard result clearly. (d) again addresses only the equilibrium outcome without the general construction.

Common Pitfalls (misconceptions, mistakes):

Using inconsistent scales; not preserving directions; confusing the meaning of a closed polygon (equilibrium) versus an open polygon (nonzero resultant).

Final Answer:

If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant is represented in magnitude and direction by the closing side of the polygon.