- You have a homework due today.
- An example problem, in which we need a "shadow casting" function: Eratosthenes and the calculation of the radius of the Earth.
-
Now let's think a little more about how we resolve the vector forces into components: we'll find it convenient to define a product of two vectors as follows:
(how would you define this for vectors in two-space?). It's just component-wise multiplication, and we add up the results.
examples:
- #1, p. 830
- #5
- #11
It turns out that
where
Otherwise, the angle is acute. examples:
- #15, p. 830
- #17
Finally then, we can put it all together to get this:
In a way, this is the "shadow" of vector u along v's direction (notice that v's length has been accounted for, by using the unit vector in the v-direction).
- Additional examples:
- #49, p. 831
- #51
- #57