Lesson: Chapter 12 — Equilibrium of Forces

12.4. Equilibrium under three non-parallel forces 4 of 6

Lines that meet at a point

For a body to be in equilibrium under three forces inclined to one another, three things must be satisfied.

(i) The three forces must be coplanar

As with parallel forces, all three must lie in one plane.

(ii) The lines of action must meet at one point

This is the new condition. It did not arise for parallel forces, whose lines of action never meet at all.

(iii) The resultant of two must equal the third

Equal in magnitude and opposite in direction.

Set against the parallel case

Condition	Three parallel forces	Three non-parallel forces
Must be coplanar	Yes	Yes
Must meet at one point	Does not arise	Yes
Resultant of two = the third	Yes	Yes

Equilibrium under three non-parallel forces

For a body to be in equilibrium under three inclined forces they must be coplanar, their lines of action must meet at one point, and the resultant of two of them must be equal and opposite to the third.