Vectors in Two and Three Dimensions
Part 9: Summary
For each of the following questions,
answer as specifically as you
can.
- What parts of the arithmetic of
numbers have a counterpart for vectors, as far as we know now?
- How are sums and differences of
vectors constructed geometrically?
- Describe in words the procedure
for resolving a vector v into its components parallel to and perpendicular
to another vector w.
- Why didn't we define the cross
product for 2-dimensional vectors?
- What can you say about the cross
product of parallel vectors? What about the cross product of perpendicular
vectors?
- What can you say about the dot
product of parallel vectors? What about the dot product of perpendicular vectors?
- In space, what differences are
there between the dot product of two vectors and the cross product of two
vectors?
- 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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