The Semester is Over

I have just finished grading calc finals, which means my first year in grad school is complete (outside of quals, which are really in the summer). However, I thought I would share some aggravating answers to what should have been a really easy problem.

Here's the setup: Vectors v and w are given, and they already calculated that they are orthogonal. The question is, does there exist a unit vector parallel to w that is perpendicular to v? If so, find it. If not, explain.

Answer: To find the vector, you need to multiply w by the reciprocal of the length of w. This is typical procedure. Since it has the same direction, it is also perpendicular to v.

Here are some "solutions"

• No, because you can't have it both ways. That is absurd.
• No, because you w is already perpendicular to v, so nothing else can be.
• No, because I'm just guessing and if I said "yes" [the professor] would want me to give some kind of bull**** explanation.