5. Vector Calculus

Surface Parameterization And Normal Vectors — Quiz

Test your understanding of surface parameterization and normal vectors with 5 practice questions.

Practice Questions

Question 1

Which of the following is a correct parameterization for the surface of a unit sphere?

Question 2

A surface is parameterized by $\mathbf{r}(u,v) = (u, v, u^2 + v^2)$. What is the vector normal to the surface at the point $(1, 2, 5)$?

Question 3

Which parameterization correctly describes the plane passing through the point $(1,2,3)$ with normal vector $\mathbf{n} = (1, -2, 1)$?

Question 4

Given the surface parameterization $\mathbf{r}(u,v) = (u \cos v, u \sin v, v)$, what is the unit normal vector at the point corresponding to $u = 1$ and $v = \frac{\pi}{4}$?

Question 5

What is the surface area element $dS$ for the parameterized surface $\mathbf{r}(u,v) = (u, v, u^2 - v^2)$?