The parallelogram rule, also called the parallelogram law, provides a straightforward means to perform vector addition with two vectors in two-dimensional space. It can also be extended to 3-dimensional or even n-dimensional space, but is most easily understood in the two-dimensional model. Simply stated, the parallelogram law states that the sum of two two-dimensional vectors P and Q can be determined by:

• drawing the vector P, then
• drawing the vector Q, taking care to place the tail of vector Q at the head of vector P, and finally
• drawing a vector S from the free tail of vector P to the free head of vector Q

This third vector S, which extends from the free tail vector P to the free head of vector Q, represents the sum of the two vectors. If the process is repeated from the same starting point--but initiated with vector...