2. Vector-Valued Functions

Vector Functions — Quiz

Test your understanding of vector functions with 5 practice questions.

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Practice Questions

Question 1

Which of the following best describes a vector-valued function?

Question 2

If $\mathbf{r}(t) = \langle t^2, \sin(t), e^{t} \rangle$, what is $\mathbf{r}'(t)$?

Question 3

Consider the vector function $\mathbf{r}(t) = \langle 3t - 2, t^2, 4 - t \rangle$. What is the magnitude of $\mathbf{r}'(t)$ at $t = 1$?

Question 4

Which of the following is an example of a parametric representation of a circle of radius 2 in the $xy$-plane?

Question 5

For the vector function $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$, what is the value of $\frac{d}{dt}\left(\mathbf{r}(t) \cdot \mathbf{r}(t)\right)$ at $t = 1$?