Editing Net force (section)

== Parallelogram rule for the addition of forces ==
{{See also|Parallelogram of force}}A force is known as a bound vector—which means it has a direction and magnitude and a [[point of application]].  A convenient way to define a force is by a line segment from a point ''A'' to a point ''B''.  If we denote the coordinates of these points as '''A''' = (A<sub>''x''</sub>, A<sub>''y''</sub>, A<sub>''z''</sub>) and  '''B''' = (B<sub>''x''</sub>, B<sub>''y''</sub>, B<sub>''z''</sub>), then the force vector applied at ''A'' is given by
: <math>\mathbf F= \mathbf{B}-\mathbf{A} = (B_x-A_x, B_y-A_y, B_z-A_z).</math>
The length of the vector <math>\mathbf\bold{B}-\mathbf\bold{A}</math>
defines the magnitude of <math>\mathbf\bold{F}</math> and is given by
: <math>|\mathbf F| = \sqrt{(B_x-A_x)^2+(B_y-A_y)^2+(B_z-A_z)^2}.</math>

The sum of two forces '''F'''<sub>1</sub> and  '''F'''<sub>2</sub> applied at ''A'' can be computed from the sum of the segments that define them.  Let '''F'''<sub>1</sub>&nbsp;=&nbsp;'''B'''−'''A''' and '''F'''<sub>2</sub>&nbsp;=&nbsp;'''D'''−'''A''', then the sum of these two vectors is
: <math>\mathbf F=\mathbf F_1+\mathbf F_2 = \mathbf{B}-\mathbf{A} + \mathbf{D}-\mathbf{A},</math>
which can be written as
: <math>\mathbf F=\mathbf F_1+\mathbf F_2 = 2\left(\frac{\mathbf{B}+\mathbf{D}}{2}-\mathbf{A}\right) = 2(\mathbf{E}-\mathbf{A}),</math>
where '''E''' is the midpoint of the segment '''BD''' that joins the points ''B'' and ''D''.

Thus, the sum of the forces '''F'''<sub>1</sub> and '''F'''<sub>2</sub> is twice the segment joining ''A'' to the midpoint ''E'' of the segment joining the endpoints ''B'' and ''D'' of the two forces.  The doubling of this length is easily achieved by defining a segments '''BC''' and '''DC''' parallel to '''AD''' and '''AB''', respectively, to complete the parallelogram ''ABCD''.  The diagonal '''AC''' of this parallelogram is the sum of the two force vectors.  This is known as the parallelogram rule for the addition of forces.