Law of Triangle of Forces (equilibrium check at a point): Which statement correctly expresses this law for three coplanar concurrent forces?

Introduction / Context:
The triangle law of forces is a graphical equilibrium criterion for three concurrent coplanar forces. It is widely used in statics for quick solution of simple trusses, joints, and ring-connector problems when only three forces act at a point.

Given Data / Assumptions:

• Three forces are coplanar and concurrent (acting at a single point).
• Forces are represented by directed line segments to scale.
• Static equilibrium (resultant equals zero).

Concept / Approach:
When three forces keep a point in equilibrium, they can be arranged head-to-tail to form a closed triangle. The closure of the polygon of forces is a geometric manifestation of zero resultant. The law is a special case of the polygon of forces and is consistent with Lami’s theorem for three-force equilibrium.

Step-by-Step Solution:

Verification / Alternative check:
Lami’s theorem states F1 / sin(α) = F2 / sin(β) = F3 / sin(γ) for the angles opposite the respective forces, which is equivalent to the triangle construction in equilibrium.

Why Other Options Are Wrong:

• B: Forces along the sides of a triangle are not necessarily concurrent or in equilibrium.
• C: This is Lami’s theorem phrasing but incomplete without angle context; option A captures the triangle-law definition directly.
• D: This is the triangle law of addition for two forces (resultant), not a three-force equilibrium statement.
• E: Orthogonality is not required for equilibrium of three forces.

Common Pitfalls:
Forgetting force concurrency; mixing the triangle law of forces (equilibrium) with the triangle law of vector addition (resultant of two forces).

Final Answer:
If three forces acting at a point can be represented in magnitude and direction by the sides of a triangle taken in order, the forces are in equilibrium