The Parallelogram Law of Vector Addition states that if two vectors are represented by the sides of a parallelogram drawn from a common point, then the diagonal of the parallelogram passing through that common point represents the resultant vector of the vector addition of the two original vectors.

Mathematically, if two vectors �⃗A and �⃗B are represented by two sides of a parallelogram originating from the same point, then the vector �⃗R representing the resultant of the vector addition is given by the diagonal passing through that common point:

R=A+B

This law is based on the principles of vector addition, where vectors are added head-to-tail to find the resultant vector. The Parallelogram Law is a geometric method to visualize and compute the result of vector addition.

This law is fundamental in vector mathematics and is widely used in various scientific and engineering applications to analyze and solve problems involving multiple forces, velocities, accelerations, and other physical quantities represented by vectors.