2. Vector-Valued Functions

Vector Functions — Quiz

Test your understanding of vector functions with 5 practice questions.

Practice Questions

Question 1

Which of the following is the correct definition of a vector-valued function?

Question 2

Given the vector-valued function $\mathbf{r}(t) = \langle 2t, t^2, \sin(t) \rangle$, what is $\mathbf{r}(0)$?

Question 3

If $\mathbf{r}(t) = \langle t^3, 3t - 1, e^t \rangle$, what is the derivative $\mathbf{r}'(t)$?

Question 4

What is the magnitude of the velocity vector for $\mathbf{r}(t) = \langle \cos(t), \sin(t), t \rangle$?

Question 5

Which of the following represents the arc length of the curve defined by $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$ from $t = 0$ to $t = 1$?