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User:Prof McCarthy/Net force

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Parallelogram rule

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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=(Ax, Ay, Az) and B=(Bx, By, Bz), then the force vector applied at A is given by

The length of the vector B-A defines the magnitude of F, and is given by

The sum of two forces F1 and F2 applied at A can be computed from the sum of the segments that define them. Let F1=B-A and F2=C-A, then the sum of these two vectors is

which can be written as

where V is the midpoint of the segment C-B that joins the points B and C.

Thus, the sum of the forces F1 and F2 is twice the segment joining A to the midpoint of the segment joining the endpoints of the two forces. The doubling of this length is easily achieved by defining a segments D-B and D-C parallel to C-A and C-A, respectively. The diagonal D-A of the parallelogram ABDC is the sum of the two vectors. This is known as the parallelogram rule.