Lami's theorem: If three forces coplanar and concurrent forces acting on a particle keep it in equilibrium, then each force is proportional to the sine of the angle between the other two and the constant of proportionality is the same.

Fig 2: Coplanar and concurernt forces

For the system shown in figure 2,

Equation of equilibrium

Subtracting (2.8) from (2.7) ,

r_am × (F₂ × F₃)..........................(2.9)

Since r_am is in the direction of F₁ , we can write

F₁ × (F₂ × F₃) = 0

This implies that F₁ lies in the plane containing F₂ and F₃.Since they do not interact with each other they , they must be parallel.

If a body is in equilibrium under the action of three coplanar concurrent forces, Lami's theorem can be used.