Geometric Interpretation of the Cross Product

This worksheet illustrates the geometric significance of the cross product. Move the yellow points to adjust the vectors.
What does the vector along the [math]z[/math]-axis represent?
Note that [math]\vec{u}[/math] and [math]\vec{v}[/math] are confined to the [math]xy[/math]-plane in this worksheet. How can we be sure that [math]\vec{u}\times\vec{v}[/math] will always point along the [math]z[/math]-axis?
What does the equality of the two numerical values signify?
Adjust [math]\vec{u}[/math] and [math]\vec{v}[/math] until their cross product points downward. Now, how big is the [i]smallest positive[/i] angle from [math]\vec{u}[/math] to [math]\vec{v}[/math]?
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