Lami’s theorem — precise statement: Choose the correct statement describing Lami’s theorem for three forces acting at a point.

Introduction / Context:
Lami’s theorem is a powerful tool for solving coplanar concurrent three-force problems without resolving components. It appears frequently in truss joints, suspended bodies, and cable–pulley pin analyses.

Given Data / Assumptions:

• Exactly three forces act at a single point.
• The forces are coplanar and in equilibrium (net force zero).
• The included angles are the angles between the directions of the other two forces.

Concept / Approach:
Lami’s theorem states: For three concurrent forces in equilibrium, F1/sin(α1) = F2/sin(α2) = F3/sin(α3), where α1 is the angle between F2 and F3 (the other two), and similarly for α2 and α3. This arises from the geometry of the force triangle and the sine rule.

Step-by-Step Solution:
Check for conditions: concurrency and exactly three forces.Write proportionality: F1/sin(angle opposite F1) = F2/sin(angle opposite F2) = F3/sin(angle opposite F3).Recognize this is the precise wording in option (d).Hence, select (d) as the correct statement.

Verification / Alternative check:
Construct the closed force triangle: join force vectors head-to-tail; by the sine rule for this triangle, the sides (force magnitudes) are proportional to the sines of the opposite angles, which are the pairwise angles between the other two forces in the original system.

Why Other Options Are Wrong:

• Equal magnitudes or 120° spacing are special cases, not the general theorem.
• “Must be in equilibrium” is necessary but not a full statement of Lami’s relation.

Common Pitfalls:

• Using the angle adjacent to the force instead of the angle between the other two forces (the opposite angle in the force triangle).

Final Answer:
if the three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two