Triangle law of forces – equilibrium test If three forces acting at a point can be 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:One of the classical equilibrium criteria for concurrent coplanar forces is the triangle law. It provides a geometric way to check whether the vector sum of forces is zero without component arithmetic.

Given Data / Assumptions:

• Three non-collinear forces acting simultaneously at the same point.
• Planar vectors arranged head-to-tail in a closed polygon (triangle).
• Magnitudes represented by side lengths; directions by side orientations.

Concept / Approach:The condition for equilibrium is that the vector sum equals zero. If three vectors placed head-to-tail form a closed triangle, the final head coincides with the initial tail, which means their sum is the zero vector. This is the triangle law of forces—an immediate geometric proof of equilibrium.

Step-by-Step Solution:

Verification / Alternative check:Resolve into x and y components. If the triangle closes, each component sum equals zero: ΣFx = 0 and ΣFy = 0, confirming equilibrium.

Why Other Options Are Wrong:

• False / conditional statements: Equilibrium does not require a right triangle or equal forces; any closed triangle suffices when vectors are drawn to scale and direction.

Common Pitfalls:Taking magnitudes only and ignoring directions; the law requires both be represented faithfully and taken “in order”.

Final Answer:True