What Is the Parallelogram Law of Forces?

The parallelogram law of forces is a method of determining the resulting force when two vectors act on an object. If both vectors have the same origin, the physicist draws a line parallel to a vector beginning at the tip of the second vector, and repeats the process for the second vector. The diagonal from the beginning point of the two vectors to this intersection is the resulting force.

The parallelogram law requires the two forces to be adjacent. Another way of constructing the parallelogram is to place the origin of the second vector at the terminal point of the first. Because parallelograms have opposite sides that are congruent, the result remains the same. Although construction and measurement of the resulting vector provides a close approximation to the resulting forces, mathematically, it is possible to solve for the resultant force using either the sine law or the cosine law from geometry.

Physics views forces as vector quantities. They have both magnitude and direction. If two forces act on an object in the same direction, the vectors add. When three forces act on an object from multiple directions, the physicist determines the resultant of two forces and repeats the procedure using the vectors for the first resultant and the third force.