Study group times
One of the best ways to do your homework is with other people. You're learning a language. You want people around that you can practice speaking with, and you can practice hearing. If you can schedule this in every day, it's one of the best ways to do homework for this class.
- before 8:45 am?
- 7:45-8:45 am?
- 10:15-11:15 am?
- 11:30-12:30 ?
- 12:45-1:45 ?
- 2-3 pm ?
- 3:15-4:15 pm ?
- after 4 pm ?
Rapid Recall
- Which problems are you ready to present?
- Which problems did you sincerely attempt (spent sufficient time to develop questions if you got stuck)?
- Let $\vec u = (2,3,-1)$ and $\vec v = (-4,1,7)$. Compute the dot product $\vec u\cdot \vec v$.
- Using the same vectors as above, compute $\vec u\cdot \vec u$.
- Using the same vectors as above, compute the magnitude $\left|\vec u\right|$.
Group problems
- Use the law of cosines (the dot product version $\vec u\cdot \vec v = |\vec u||\vec v|\cos\theta$), to find the angle between each pair of vectors below. Take turns doing each problem, one at a time. Remember to pass the chalk between each problem. Use a calculator to compute the inverse cosine, as needed, and make a picture to verify that your answer is reasonable.
- $(-2,1)$ and $(1,3)$
- $(2,3)$ and $(-1,4)$
- $(-5,1)$ and $(2,10)$
- $(a,b)$ and $(c,d)$ (a general formula)
- $(1,2,3)$ and $(-7,2,1)$
- $(1,2,3)$ and $(x,y,z)$.
- Give values for $x,y,z$ above so that the angle is 90 degrees.
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