5. Vector Calculus

Divergence And Curl — Quiz

Test your understanding of divergence and curl with 5 practice questions.

Practice Questions

Question 1

Given a vector field $\mathbf{F}(x,y,z) = (2x - y^2, 3y + z, x - 2z)$, what is the divergence $\nabla \cdot \mathbf{F}$?

Question 2

Consider the vector field $\mathbf{G}(x,y,z) = (yz, xz, xy)$. What is the curl $\nabla \times \mathbf{G}$?

Question 3

If $\mathbf{F}(x,y,z) = (xy, yz, zx)$, what is the value of $\nabla \cdot \mathbf{F}$ at the point $(1,2,3)$?

Question 4

Which of the following vector fields is conservative (i.e., its curl is zero)?

Question 5

Consider $\mathbf{F}(x,y,z) = (x^2, y^2, z^2)$. What is the divergence $\nabla \cdot \mathbf{F}$?