What Is the Parallelogram Law in Physics?

In physics, the parallelogram law is a rule that states that if two vectors are adjacent to one another, then they can be added together head to tail to find the resultant by drawing a line that connects the vector with the free tail to the vector with the free head. The line that connects these vectors is the resultant vector, which also is the diagonal of a parallelogram.

If a student needs to find a resultant vector quantity R of the vectors A and B, a useful formula to use is that vector R = vector A + vector B. When drawing these three vectors, a triangle shape is formed with three angles alpha, beta and theta. Using these three angles and the sine law, the resultant is found as (R/sin theta) = (vector A /sin alpha) = (vector B/sin beta), where angles alpha, beta and theta are the angles opposite the vectors A, B and R, respectively. The resultant vector also can be found using the cosine law.