A surface, a tangent plane, a normal line

I set out to do a visualization that is basic to the multivariable calculus classroom:  plot a surface, a tangent plane, and a normal line.  I didn’t do it on the first try…or the second.

I had to learn some things about the draw3d functionality in Maxima and wxMaxima.  Here’s a great resource by Wilhelm Haager.  In the end I’m delighted at the amazing flexibility of that command, but still scratching my head a little about how this would appear to an otherwise uninitiated beginner to Maxima.

Here’s the html export of my session.