finding out if two vectors are perpendicular or parallel I'm not sure if I quite get this.  For example, 
(1, -1) and (-3, 3)
take the cross product, you will end up with
-3 + (-3)
This doesn't equal 0, so it's not perpendicular. So that leaves me with it being parallel. When are two vectors parallel?

They are parallel if and only if they are different by a factor i.e. (1,3) and (-2,-6). 
The dot product will be 0 for perpendicular vectors i.e. they cross at exactly 90 degrees. 
When you calculate the dot product and your answer is non-zero it just means the two vectors are not perpendicular.
