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] Give parametric equations for the line through $(2,1,-5)$ that is parallel to $⟨1,5,-1⟩$.
2. [3 points] Give a vector equation for the line at the intersection of planes $x+2y-5z=5$ and $3x-2y+z=-1$.

3. Let $S$ be the plane $2x-y+z=1$ and let $P$ be the point $(4,2,1)$.

   1. [3 points] Find the distance between $S$ and $P$.
   2. [1 point] Find the point on $S$ that is closest to $P$.