Ignoring zero, one can say that a scaler is represented by either a
positive or a negative number. Likewise, ignoring boundaries, one can
say that the ending of a 2D vector is in one of the four quadrants.
For a 3D dimensional vector the ending of a vector (the tip of the
arrow) is in one of the eight "regions."
Replacing the word "region" by "quadrant" is not acceptable. What word
should I use?