Editing Resultant force (section)

==Torque-free resultant==
It is useful to consider whether there is a point of application '''R''' such that the associated torque is zero.  This point is defined by the property
:<math> \mathbf{R} \times \mathbf{F} = \sum_{i=1}^n \mathbf{R}_i \times \mathbf{F}_i, </math>
where '''F''' is resultant force and '''F'''<sub>i</sub> form the system of forces.

Notice that this equation for '''R''' has a solution only if the sum of the individual torques on the right side yield a vector that is perpendicular to '''F'''.  Thus, the condition that a system of forces has a torque-free resultant can be written as
:<math>\mathbf{F}\cdot(\sum_{i=1}^n \mathbf{R}_i \times \mathbf{F}_i )=0.</math>
If this condition is satisfied then there is a point of application for the resultant which results in a pure force.  If this condition is not satisfied, then the system of forces includes a pure torque for every point of application.