Parallelogram Rule for Vector Addition
If $\mathbf{v}$ and $\mathbf{w}$ are vectors in 2 -space or 3 -space that are positioned so their initial points coincide, then the two vectors form adjacent sides of a parallelogram, and the $\operatorname{sum} \mathbf{v}+\mathbf{w}$ is the vector represented by the arrow from the common initial point of $\mathbf{v}$ and $\mathbf{w}$ to the opposite vertex of the parallelogram.
