Directions:

1. Section: Math251-007
2. Write your name with one character in each box below.
3. Show all work. No credit for answers without work.

1. [3 points] Find the unit vector in the same direction as $2𝐢-3𝐣+6𝐤$. Simplify as much as possible.
2. [3 points] Find the vector with magnitude $6$ in the same direction as $\overrightarrow{\mathit{𝑃𝑄}}$, where $P=(5,2,-1)$ and $Q=(1,2,1)$.
3. [2 points] Find a simplified equation in variables $x$, $y$, and $z$ whose solution set equals the points $(x,y,z)$ that are equally distant from $(1,-1,3)$ and $(0,0,0)$.

4. [2 points] Vectors $𝐚$, $𝐛$, and $𝐜$ are shown below. Find a formula for $𝐜$ in terms of $𝐚$ and $𝐛$.