Equilibrium of two forces at a point: If two forces act at a point and the system is in equilibrium, what must be true about their magnitudes and directions?

Introduction / Context:
Equilibrium under two forces is a foundational result in statics. When only two forces act on a rigid body and it remains in equilibrium, those forces must be strictly collinear, equal in magnitude, and opposite in direction so that both resultant force and resultant moment are zero.

Given Data / Assumptions:

• Rigid body assumption.
• Only two forces act on the body.
• No couple acting separately.

Concept / Approach:

For ΣF = 0 in vector form with only two forces F1 and F2, we must have F1 + F2 = 0 → F2 = −F1, which implies equal magnitudes and opposite directions along the same line. Also, ΣM about any point is then zero because their lines of action are coincident (no net moment arm).

Step-by-Step Solution:

Verification / Alternative check:

Non-collinear equal and opposite forces produce a couple, violating equilibrium; perpendicular forces cannot cancel each other fully.

Why Other Options Are Wrong:

(a) same sense cannot balance; (c) perpendicular forces cannot yield zero resultant; (d) incorrect; (e) requires an additional force to balance the components.

Common Pitfalls:

Confusing “same line” with “parallel but not collinear”; forgetting that equal and opposite but non-collinear forces create a pure moment.

Final Answer:

Equal in magnitude and along the same line in opposite sense