NOTE For a surface defined by $r=f(u,v)$, where $(u,v)\in \text{U}\subseteq R^{\text{2}}$, the tangent plane at point r(u₀, v₀) is defined by the vectors ${\left(\frac{\partial f}{\partial u}\right)}_{\begin{array}{l}u=u_0\\ v=v_0\end{array}}$ and ${\left(\frac{\partial f}{\partial v}\right)}_{\begin{array}{c}u=u_0\\ v=v_0\end{array}}$ if they are linearly independent.