Vectors in Two and Three Dimensions

Part 9: Summary

For each of the following questions, answer as specifically as you can.

1. What parts of the arithmetic of numbers have a counterpart for vectors, as far as we know now?
2. How are sums and differences of vectors constructed geometrically?
3. Describe in words the procedure for resolving a vector v into its components parallel to and perpendicular to another vector w.
4. Why didn't we define the cross product for 2-dimensional vectors?
5. What can you say about the cross product of parallel vectors? What about the cross product of perpendicular vectors?
6. What can you say about the dot product of parallel vectors? What about the dot product of perpendicular vectors?
7. In space, what differences are there between the dot product of two vectors and the cross product of two vectors?
8. Why is it easy to differentiate vector-valued functions? How is the calculation related to what you know about finding derivatives of ordinary functions?

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Copyright CCP and the author(s), 2001-2002