Let $P=(1,0,3)$ and $Q=(0,2,-1)$ and $R=(1,1,1)$.
- We know that $\vec {PR}=(0,1,-2) $. Give a unit vector that points in the same direction as $\vec{PR}$, then give a vector of length 3 that points in the same direction.
- Give a vector equation of a line that passes through $Q$ and is parallel to $\vec{PR} $.
- Give a vector equation of the line that passes through $P$ and $Q$.
- Compute the dot product $\vec{PQ}\cdot \vec{PR}$.
- Find the angle between $\vec{PQ}$ and $\vec{PR}$.
- Find 4 vectors that are orthogonal to $ (2,4,-7) $.
- Draw the vector field $\vec F(x,y) = (2x+y,x+2y)$.
- Draw the vector field $\vec F(x,y) = \langle y,-x\rangle$.
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