visualizing vector calculus and analytic geometry

El mi?, 25-02-2009 a las 22:54 +0100, josh escribi?:
> Hi,
> 
> I'm a public schools math teacher (in Germany) and I'll be teaching a
> unit on analytical geometry in my 12 grade math course.
> 
> What I like to be able to do is to simply and quickly manipulate and
> visualize vectors and planes and lines in R^3 using different
> representations (parametric, vector, etc.), e.g. enter vectors and have
> them appear in R^3, then e.g. multiply the vectors with a scalar, and
> see them get longer, subtract two vectors and see the difference vector,
> visualize parameter and vector rep. of planes and lines and their
> intersection etc., not just plotting 3d surfaces of f(x,y).
> 
> I've tried the plotting in maxima, and I can't get it to plot single
> points or vectors, just surfaces of f(x,y). The plotting in maxima
> requires entering lots of parameters and I've not even found a way to
> plot vectors, let alone easily manipulate them and  see the changes
> quickly (I want to do this live in class, e.g. quickly entering the
> vector and seeing it in R^3). I've also found no way to enter vectors,
> or vector representations of lines and planes.
> 
> Can maxima do this? How?! If not, does anybody know of a usable free
> software which can manipulate and visualize vectors, planes, etc. in 3d?

Here are some examples:

http://www.telefonica.net/web2/biomates/maxima/gpdraw/vectors


-- 
Mario