- Homework 13.2 is due
- Remember to look over the exam again, correcting your errors, and see me for 40% of your missed points back.
- We'll start today with a quiz over 13.3 -- the dot product
- We'll plan to have a review session Monday evening, prior to the final. This will be question and answer. Let's say 7:00-9:00, in this room (if we need to move, I'll post a sign).
- Read Section 13.4 for next Tuesday responding to the worksheet for section 13.4. There will be a quiz next Thursday over the reading.
- Homework for section 13.3 will be due next Thursday.
- We have looked at examples like #58, p. 665:
- First and foremost: Newton's laws of motion (in particular
), and statics.
- The parallelogram rule
- We can think of the force vectors on the cables as being composed of vector components (as well as coordinate components).
It turns out that we could see the solution very easily; calculating the force vectors was a little more complicated.
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. 680 (and let's practice drawing the line connecting the tips of these two position vectors)
- #6, p. 680
- #11, p. 681
It turns out that
where
Otherwise, the angle is acute. examples:
- #23, p. 681
- Now: here's problem that really shows the power of this concept: #60, p. 681
Finally then, we can put it all together to get this:
- First and foremost: Newton's laws of motion (in particular
- Additional examples:
- #53, 54, p. 681
- #70, p. 682