Chapter 14.4, Problem 49ES

Determine whether the statement is true or false. Explain your answer.

If $\text{r}\left(u,v\right)=x\left(u,v\right)\text{i}+y\left(u,v\right)\text{j}+z\left(u,v\right)\text{k}$ such that $\partial \text{r}/\partial u\text{and}\partial \text{r}/\partial v$ are nonzero vectors at $\left(u_0,v_0\right),$ then

$\frac{\partial \text{r}}{\partial u}\times \frac{\partial \text{r}}{\partial v}$

is normal to the graph of $\text{r}=\text{r}\left(u,v\right)\text{at}\left(u_0,v_0\right).$