Parallelogram Law


The parallelogram law gives the rule for vector addition of vectors A and B. The sum A+B of the vectors is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

Let |·| denote the norm of a quantity. Then the quantities x and y are said to satisfy the parallelogram law if


If the norm is defined as |f|=sqrt(<f|f>) (the so-called L2-norm), then the law will always hold.

See also

L2-Norm, Norm, Vector, Vector Addition

Explore with Wolfram|Alpha


Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 1-2, 1985.Jeffreys, H. and Jeffreys, B. S. Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 58, 1988.

Referenced on Wolfram|Alpha

Parallelogram Law

Cite this as:

Weisstein, Eric W. "Parallelogram Law." From MathWorld--A Wolfram Web Resource.

Subject classifications