2. Vector-Valued Functions

Curvature And The Tnb Frame — Quiz

Test your understanding of curvature and the tnb frame with 5 practice questions.

Practice Questions

Question 1

Which of the following represents the formula for the curvature $\kappa$ of a smooth vector-valued function $\mathbf{r}(t)$ in three dimensions?

Question 2

Given a vector function $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$, what is the curvature $\kappa$ at $t = 0$?

Question 3

Which of the following correctly describes the unit tangent vector $\mathbf{T}(t)$?

Question 4

If the curvature $\kappa$ of a curve is constant and nonzero, and the torsion $\tau$ is zero, what type of curve is it?

Question 5

What is the binormal vector $\mathbf{B}(t)$ defined as in the Frenet–Serret frame?