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. Find an equation of the set of all points equidistant from the points (-1,5,3) and (6,2,-2).
 
 

[3 pts] 2. If a = <2,-3,1>, b = <7,-1,2>, and c = <2,1,-1>, find the angles (give both exact values and decimal approximations) between each pair of vectors.
 
 

[3 pts] 3. Find a unit vector in the direction of the vector b from problem 2.
 
 

[3 pts] 4. Find a vector of length 3 which is perpendicular to the vector c from problem 2.
 
 

[3 pts] 5. Find a vector which is perpendicular to both vectors a and c from problem 2.