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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 -axis represent?

Note that and are confined to the -plane in this worksheet. How can we be sure that will always point along the -axis?

What does the equality of the two numerical values signify?

Adjust and until their cross product points downward. Now, how big is the smallest positive angle from to ?