Question
Find an equation of the tangent plane to the given parametric surface at the specified point. Graph the surface and the tangent plane.$ \textbf{r}(u, v) = (1 - u^2 - v^2) \, \textbf{i} - v \, \textbf{j} - u \, \textbf{k} $; $ (-1, -1, -1) $
Step 1
These are given by: $\textbf{r}_u = \frac{\partial \textbf{r}}{\partial u} = -2u \, \textbf{i} - \textbf{k}$ $\textbf{r}_v = \frac{\partial \textbf{r}}{\partial v} = -2v \, \textbf{i} - \textbf{j}$ Show more…
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