Chapter 14.7, Problem 13ES

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

If $\text{r}=x\left(u,\upsilon \right)\text{i}+y\left(u,\upsilon \right)\text{j},$ then evaluating $\left|\partial \left(x,y\right)/\partial \left(u,\upsilon \right)\right|$ at a point $\left(u_0,{\upsilon }_0\right)$ gives the perimeter of the parallelogram generated by the vectors $\partial \text{r}/\partial u\text{and}\partial \text{r}/\partial \upsilon \text{at}\left(u_0,{\upsilon }_0\right).$