For the equilibrium of rigid bodies in two-dimensions or in three dimensions the algebraic sum of all the external forces should be zero and also the algebraic sum of moments of all the external forces about any point in their plane should be zero. Mathematically it is expressed by the equations:

= 0 and M = 0

The sign * *is known as sigma which represents the algebraic sum of forces or moments

*(i) *For two-dimensional bodies, the forces are written as

*F _{x} *= 0 and

*F*= 0

_{y}*(ii) *For three-dimensional bodies, the forces are expressed as

*F _{x} *= 0,

*F*= 0 and

_{y}*F*= 0

_{z}*F _{x} *= Algebraic sum of all components of forces in

*x*-direction,

*F _{y} *= Algebraic sum of all components of forces in

*y*-direction, and

*F*= Algebraic sum of all components of forces in

_{z}*z*-direction.

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