Dot product discovery applet
We denote the dot product of two vectors u and v in Rn as u•v. Use the applet below to discover the basic properties of the dot product. The questions below the applet are intended to guide your discovery.
- Is u•v a vector or a scalar?
- When is u•v positive, negative, and zero?
- What happens to u•v when u or v gets longer?
- Is the dot product commutative? That is, is u•v=v•u?
- What is u•u?
Check the box labeled "Show the unit circle."
- Fix one vector on the unit circle. Move the other vector around the circle and observe u•v. u•v can be expressed as a familiar, elementary function. What do you think it is?
- Is this still true if u and v aren't unit vectors?
Created by David Richeson using GeoGebra.