–

For discussion sake, let’s say a body experiences three and only three forces, *F*_{1}, *F*_{2} and *F*_{3}.

Remember that if a body is in static equilibrium, the summation of moments **about any point** must be zero.

Let’s exercise our freedom to choose our pivot point wherever we like. Let’s choose point X, where the lines of action of *F*_{1} and *F*_{2} intersect. Can you see that if the line of action of *F*_{3 }does not pass through point X, then the summation of moments about X will not be zero!?! Because *F*_{1} and *F*_{2} both contribute zero moment about X, *F*_{3} must also contribute zero moment. The only way for *F*_{3} to contribute zero moment about X is if its line of action also passes through X.

Thus with this simple logic, we arrive at this rather cute rule that for a three-force system at static equilibrium, (the lines of action of) all three forces must intersect at one common point. 🙂

P.S. This rule is not applicable if all three forces are parallel to one another. Why?

P.S. This rule is also not applicable if a body experiences 4 or more forces. Why?

P.S. If you prefer to hear me explain, click here.