**Resultant of
Coplanar Forces:** When we are examining a system involving two
or more forces, we are usually interested in finding the resultant
force in terms of its magnitude as well as direction. The
graphical, trigonometric, and vector approaches discussed earlier
can be applied to problems involving coplanar (two-dimensional) forces. We will
expand on this discussion with the help of the following
examples.

**Resultant of
Non-Coplanar Forces:** The discussion in this section applies
mainly to systems involving more than two concurrent forces. A
simple experiment of holding two pencils (as a model of two
vectors) end to end and rotating them around at various angles will
show that two concurrent vectors are always coplanar. Therefore, we
could use the graphical approach in finding the resultant. The
complexity arises, however, when the two forces are located in a
plane other than xy, xz, or yz plane, or when the system involves
three or more non-coplanar forces. In that case, it would be easier
to use trigonometric or vector approach to find the resultant
force. Here, we make use of direction cosines and/or unit vector to
help define the exact direction of a force vector. The analysis of
such a system is demonstrated in the following examples.