I would need some basic vector mathematics constructs in an application. Dot product, cross product. Finding the intersection of lines, that kind of stuff.
I can do
Re-check that ol'good friend of C++ programmers called Boost. It has a linear algebra package that may well suits your needs.
Check www.netlib.org, which is maintained by Oak Ridge National Lab and the University of Tennessee. You can search for numerical packages there. There's also Numerical Recipes in C++, which has code that goes with it, but the C++ version of the book is somewhat expensive and I've heard the code described as "terrible." The C and FORTRAN versions are free, and the associated code is quite good.
There is a nice Vector library for 3d graphics in the prophecy SDK:
Check out http://www.twilight3d.com/downloads.html
For an extremely lightweight (single .h file) library, check out CImg. It's geared towards image processing, but has no problem handling vectors.
For linear algebra: try JAMA/TNT . That would cover dot products. (+matrix factoring and other stuff) As far as vector cross products (really valid only for 3D, otherwise I think you get into tensors), I'm not sure.
I would stay away from using NRC code for anything other than learning the concepts.
I think what you are looking for is Blitz++