Each problem is worth the indicated number of points. For full credit you must give an appropriate explanation of your reasoning. Submissions must be legible to receive credit.

[3 pts] 1. If P is the point (-1,5,3) and Q is the point (6,2,-2), find an equation for the plane through the midpoint of segment PQ and with vector PQ as its normal vector.
 

[3 pts] 2. Find an equation for the plane through the points (2,0,0), (0,3,0), and (0,0,6).
 

[3 pts] 3. Write parametric and vector equations for the line from (-3,5,2) to (1,7,-1).
 

[3 pts] 4. Find an equation for the plane containing the lines r = <1,1,0>+t<1,-1,2> and r = <2,0,2>+s<-1,1,0>.
 

[3 pts] 5. Find an equation for the line perpendicular to the plane 2x-3y+z = 1 which passes through the origin.