Standard Position of a Quaternion?

Question

In 2D, the standard position of a vector is down the positive X axis. Is there an equivalent position for quaternions?

Answer 1

There is no "standard position of a vector." In 2D or 3D.

There is of course a general mathematical convention that the X,Y direction of an angle is (cos(angle), sin(angle)). Which means that if the angle is 0, then the vector points down the positive X axis. But that's far from a "standard position of a vector."

While quaternions can seem like a 3D angle in some math operations, they are not angles. Quaternions (in terms of graphics) represent the orientation of a space, relative to another space.