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)?
- Give a vector equation of a line that passes through $(1,2)$ and is parallel to $(3,4)$.
- Give a vector of length 4 that is parallel to the vector $(-1,2,-2)$.
- Use the law of cosines ($c^2=a^2+b^2-2ab\cos\theta$) to find the angle between the vectors $(-1,5)$ and $(2,4)$.
Group problems
- 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 2 units in the direction of $\vec v=(-4,5,1)$. Give an equation for the position $(x,y,z)$ at any time $t$.
- Use the law of cosines ($c^2=a^2+b^2-2ab\cos\theta$ or $\vec u\cdot \vec v = |\vec u||\vec v|\cos\theta$) to find the angle between each pair of vectors below.
- $(-2,1)$ and $(1,3)$.
- $(2,3)$ and $(-1,4)$
- $(\pi,e)$ and $(\sqrt{17},c)$
- $(1,2,3)$ and $(-7,2,1)$
- $(1,2,3)$ and $(x,y,z)$.
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