I came up with this while thinking about the
recent solenoid question, but the puzzle is
more general than that.
Assume you are working in D dimensions, where
D >= 2.
1) Given a set of D-1 mutually perpendicular
vectors, construct a vector that is perpendicular
to each of the others.
Hint: When D=3, you can simply take the cross
product.
Hint: When D=2, you can simply rotate the
vector 90 degrees in the plane.
The objective is to find a simple and elegant
method that works for all D.
2) Extra credit if your solution works in a
D-dimensional Minkowski space, i.e. where we
have D-1 spacelike dimensions and 1 timelike
dimension.
The usual jsd puzzle rules apply: This is not
meant to be a trick question or word game. The
answer does not involve finding any hidden or
twisted meaning in the wording of the question.
There exists an answer that is useful and IMHO
interesting. There may be more than one way
of solving the puzzle. Everything I've said,
including the hints, is AFAIK true and helpful.
On the other hand, I haven't told you everything
I know about the puzzle; for example I haven't
told you the answer.