Applied Mechanics and Graphic Statics
A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if

Floor and wall both are smooth surfaces
Floor is rough and the wall is smooth
Floor and wall both are rough surfaces
Floor is smooth and the wall is rough

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Applied Mechanics and Graphic Statics
The Law of Polygon of Forces states that

If a polygon representing the forces acting at point in a body is closed, the forces are in equilibrium
If forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side
If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by t
If forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium

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