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
Applet links
This applet is found in the pages
General information about Geogebra Web applets
This applet was created using Geogebra. In most Geogebra applets, you can move objects by dragging them with the mouse. In some, you can enter values with the keyboard. To reset the applet to its original view, click the icon in the upper right hand corner.
You can download the applet onto your own computer so you can use it outside this web page or even modify it to improve it. You simply need to download the above applet file and download the Geogebra program onto your own computer.