Triangle law of forces – equilibrium condition\nIf three concurrent forces are represented in magnitude and direction by the three sides of a triangle taken in order (head-to-tail), are the forces in equilibrium?

Introduction / Context:
The triangle law of forces provides a graphical equilibrium test for three concurrent coplanar forces. If the vector sum of forces is zero, a closed polygon (triangle for three forces) results.

Given Data / Assumptions:

• Three forces act at a common point.
• Vectors are drawn to scale, in magnitude and direction.
• Sides are taken in order (head-to-tail construction).

Concept / Approach:
Equilibrium occurs when the resultant of all forces is zero. Graphically, placing force vectors head-to-tail to form a closed triangle ensures that the final head coincides with the initial tail, implying zero resultant.

Step-by-Step Solution:

Verification / Alternative check:
Analytically, resolve the three forces into perpendicular components. If the component sums are zero in both axes, the vector polygon closes; both methods are equivalent.

Why Other Options Are Wrong:

• ‘‘No’’: contradicts the triangle law of forces.
• Conditions about right angle or equal forces are unnecessary; any closed triangle suffices.

Common Pitfalls:
Forgetting to take vectors in order, or mis-scaling directions so the polygon does not represent the actual forces.

Final Answer:
Yes