## Cross product discovery appletThe cross product of two vectors u and v in R
Note: in the applet below, the vectors u and v live in R Discovery questions: - Is uxv a vector or a scalar?
- Is the cross product commutative? That is, is uxv=vxu?
- When does uxv point out of the screen and when does it point into the screen?
- When is uxv the zero vector?
- What happens to uxv when u or v gets longer?
- What is (uxv)•u? (uxv)•v?
- What is |uxv| when u and v are orthogonal vectors?
Check the box labeled "Show the unit circle." - Fix one vector on the unit circle. Move the other vector around the circle and observe |uxv|. |uxv| 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?
Check the box labeled "Show parallelogram." - What do you notice?
Created by David Richeson using GeoGebra. |