Answer
$\displaystyle \mathrm{r}(t)=\mathrm{i}+\frac{1}{\sqrt{t}}\mathrm{k}$
Work Step by Step
Parametric equations: $\mathrm{r}(t):\quad\left\{\begin{array}{ll}
x=t & \\
y=1 & \\
y=2t^{1/2} &
\end{array}\right.$
Differentiate $(\displaystyle \frac{d}{dt})$ each component function
$\mathrm{r}^{\prime}(t):\quad\left\{\begin{array}{l}
x=1\\
y=0\\
z=2(\frac{1}{2}t^{-1/2})=\frac{1}{\sqrt{t}}
\end{array}\right.$
$\displaystyle \mathrm{r}(t)=\mathrm{i}+\frac{1}{\sqrt{t}}\mathrm{k}$
