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 $\mathbf{F}(x,y,z) = (2x, -3y, 4z)$, what is the divergence $\nabla \cdot \mathbf{F}$?

Question 2

If $\mathbf{F}(x,y,z) = (y^2, 2xz, z^3)$, what is the curl $\nabla \times \mathbf{F}$?

Question 3

Consider the vector field $\mathbf{G}(x,y,z) = (e^x, \sin(y), \cos(z))$. What is the divergence $\nabla \cdot \mathbf{G}$?

Question 4

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

Question 5

If $\mathbf{H}(x,y,z) = (x^2y, y^2z, z^2x)$, what is the divergence $\nabla \cdot \mathbf{H}$?