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)?
- Using the vectors on the board, draw $\vec u+\vec v$ and $\vec u-\vec v$.
- Give the component form of a vector of length 2 that is parallel to $\left<3,4\right>$.
- Draw and shade the region in space satisfying $0\leq z\leq 5$ with $x=2$.
Group problems
- For this one, have everyone in the group use chalk at the same time. In 3D, plot the points $(1,2,0)$, $(1,0,3)$, $(0,2,3)$, $(1,2,3)$, $(-2,4,-3)$.
- Give the component form of a vector that points from $(1,2,3)$ to $(-2,4,9)$.
- Give a vector equation of the line that passes through the point $(1,2,3)$ and $(-2,4,9)$ (all distances are in meters).
- Modify your vector equation from the previous part so that the speed of an object that is tracked with this equation is 3 meters per unit time.
- An object starts at $P=(1,2,3)$ and each unit of time its displacement is $\vec v=(-4,5,1)$. Give an equation for the position $(x,y,z)$ at any time $t$.
- Use the law of cosines ($c^2=a^2+b^2-2ab\cos\theta$) to find the angle between the vectors $(-2,1)$ and $(1,3)$.
- Use the law of cosines to find the angle between the vectors $(1,2,3)$ and $(-2,4,9)$.
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