Well, I was thinking about dot3 extension and had some ideas ;D. I thought it would be cool if there was a cross_product function. This could be used with dot3 for some cool shadings. The whole reason is it could be hardware accelerated, as the cross product is used alot in three-d apps (at least alot I know of).
Thinking of this, and realizing that alot of people use cool algorithms to produce special effects and shading–I wonder if the pixel shaders and vertex shaders will be able to be as fast as just hardcoding some realy useful algs into the graphics cards. 
Just my 2 cents worth, be as brutal as you want. 
ARB_fragment_program has a XPD instruction to do a cross product.
bakery2k: you’re right but it’s a bit heavy. A light extension like ARB_texture_env_cross_product (which looks like ARB_texture_env_dot3) would be easier to use and could probably be implemented on a wide range of hardware (whereas ARB_fragment_program can only be implemented on elite hardware)
The whole “texture_env” paradigm dies with OpenGL 1.0. That’s fine; it was a hack anyway. There’s no need to further the support for more “texture_env” hacks, when all the hardware that implements them also implement ARB_fragment_program.