next up previous
Next: About this document Up: MA 1004 Laboratory Previous: Background


  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