- Use Maple to compute the following, given that and .
- .
- .
- .
- .
- .
- .

- 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.

- Find a vector perpendicular to such that
where and .

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

Wed Mar 22 12:52:33 EST 1995