While the "Amazing Images" from Prof. Birkeland sure is ingenious and you can do things using it which you never thought Mathcad would be able to, its sure not easy food. You would have to spend quite some time studying the routines and methods used in this handbook.
I doubt that you can easily create the kind of plots your screenshot shows with it.
Plotting just a few spheres and planes could be achieved easier with Mathcad without the "Amazing" toolbox, even with transparency effects. Plotting vectors can be done but requires a bit more work. The overall look will not come that close to what you show, though, and sure will not be achieved so easy and intuitive as with GeoGebra.
Why don't you stick to GeoGebra for plots like this? After all its a brilliant piece of software and its free.
