Sorry, I must not have been clear. The three functions f, g, and h are each from \mathbb{R}^2\rightarrow\mathbb{R}^3. That is, they each have coordinate functions f_i, g_i, and h_i (f, g, and h are not the coordinate functions of some F:\mathbb{R}^2\rightarrow\mathbb{R}^3). The use of the...
Not really a homework problem... just a general question (this seemed like the place to put it...). Say I have three functions:
f,g,h:\mathbb{R}^2\rightarrow\mathbb{R}^3
and an expression along the lines of:
\left\langle f(u_1,u_2),g(u_1,u_2)\right\rangle h(u_1,u_2)
What...