This applet demonstrates the dot product, which is an important concept in linear algebra and physics. The goal of this applet is to help you visualize what the dot product geometrically.

Two vectors are shown, one in red (A) and one in blue (B). On the right, the coordinates of both vectors and their lengths are shown. The projection of A onto B is shown in yellow, and the angle between the two is shown in orange.

At the bottom of the screen are four bars which show the magnitude of four quantities: the length of A (red), the length of B (blue), the length of the projection of A onto B (yellow), and the dot product of A and B (green). Some of these quantities may be negative.

To modify a vector, click on its arrowhead and drag it around. To swap A and B, click the swap button. Swapping the two does not change the dot product.

Matrix Applet.

More applets.

Huge thanks to Bob Hanson and his team for converting this applet to javascript.