# Math Insight

### Applet: The sum of two vectors

The sum $\vc{a}+\vc{b}$ of the vector $\vc{a}$ (blue arrow) and the vector $\vc{b}$ (red arrow) is shown by the green arrow. As vectors are independent of their starting position, both blue arrows represent the same vector $\vc{a}$ and both red arrows represent the same vector $\vc{b}$. The sum $\vc{a}+\vc{b}$ can be formed by placing the tail of the vector $\vc{b}$ at the head of the vector $\vc{a}$. Equivalently, it can be formed by placing the tail of the vector $\vc{a}$ at the head of the vector $\vc{b}$. Both constructions together form a parallelogram, with the sum $\vc{a}+\vc{b}$ being a diagonal. (For this reason, the commutative law $\vc{a}+\vc{b}=\vc{b}+\vc{a}$ is sometimes called the parallelogram law.) You can change $\vc{a}$ and $\vc{b}$ by dragging the yellow points.

Applet file: vector_sum.ggb