The problem:

Let be the inverse of stereographic projection from to the equatorial hiperplane . Show that for every vector exists such that

.

The solution must rely on the following hint: the vector part of is , where .

I can't even get this vector part right..

As always, thanks for all the hints and help.

I will continue to work on it and post if I get anything.

(If it matters, it's not homework or exam question, just exercise.)