On friday, we talked about the dot products of vectors. Overall, most of the class wondered why we needed to divide by the vector length (at this time, radical 80) in order to find B-hat. The explanation was in order to make the vector equal to one of its own unit, but having been used to standardized units I and many others still sat there dazed and confused. BUT! once I thought it over, I realized we were just converting the "unit-1's" that the vectors were in into our own unit dictated by the vectors length (making vector B's length a unit).
The ding moment specifically was " OH we're making our own set of feet/inches/yards/etc out of the length of vector B" *facepalm* better explained as: vector B becomes your new 'meters' by which you define the dot product of B and A. And the reason we need it to be labelled B-hat is BECAUSE it becomes 1 'length b' which can be converted back to radical-80 "unit-1's" by which the vectors were originally measured.
First "ding" moment. 3rd day of school, I think I'm making progress.