**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.