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## Exercises

1. Use Maple to compute the following, given that and .
1. .
2. .
3. .
4. .
5. .
6. .

2. If and are the vectors from the previous exercise, explain why it is true that

Note - just computing both sides of the equation and comparing is not a sufficient explanation. Your explanation must include references to properties of the cross product.

3. Find a vector perpendicular to such that

where and .

4. Show that, in general, is not equal to . Remember that just showing that the results are not the same for specific fixed vectors is not enough. Instead, you should do the calculations with arbitrary three-dimensional vectors.

5. Show that is perpendicular to and perpendicular to , where and are arbitrary three-dimensional vectors.

6. Verify the vector identity

where and are arbitrary three-dimensional vectors, and then explain how this identity implies the equation

where is the angle between and .

William W. Farr
Wed Mar 22 12:52:33 EST 1995