The vector function given is:

$\vec{r}(t) = \sqrt{2t} \, \hat{i} + e^t \, \hat{j} + e^{-t} \, \hat{k}$

with the domain $0 \leq t \leq 9$.

Let me know if you need more details or have any questions.

Here are five relative questions for further exploration:

1. What is the magnitude of this vector function at $t = 9$?
2. How does the vector behave as $t \to 0$?
3. What is the derivative of this vector function with respect to $t$?
4. Can you compute the unit vector corresponding to this vector function?
5. What is the dot product of this vector with another given vector?

Tip: When dealing with vector functions, always consider evaluating them at key points (like $t = 0$ or $t = 9$) to understand their behavior.