Exploratories   Dot Product


The Dot Product applet shows how the scalar dot product value of two vectors depends on both the vectors' lengths and the angle between them. It also demonstrates the dot product's property of rotational invariance. Editable equations are displayed, as are concept explanations and help text. The dot product is an essential building block in linear algebra and for doing almost any type of transformation or rendering in computer graphics.


Easily usable by both undergraduates and high school students in any course using the dot product (e.g., linear algebra, physics, graphics programming, etc.).


Users click and drag on the vector arrows (to reposition the end of the vector) and stems (to rotate the vector). The dot product value is shown with a thermometer-style display, as well as in an equation format, along with the vector coordinates. The arc representing the angle between the vectors can be clicked and dragged to rotate both vectors at the same time and show the rotational invariance.