Chapter 13.4, Problem 51E

To determine

To calculate:

Normal vector $\left(\overrightarrow{N}\right)$ at the point indicated use the equation:

$\overrightarrow{N}\left(t\right)=\frac{\text{u}\left(t\right)\overrightarrow{r}"\left(t\right)-u\text{'}\left(t\right)\overrightarrow{r}\text{'}\left(t\right)}{\Vert u\left(t\right)\overrightarrow{r}"\left(t\right)-u\left(t\right)\overrightarrow{r}\text{'}\left(t\right)\Vert }$

$\overrightarrow{r}\left(t\right)=\left(t,e^t,t\right)\text{ at }t=0$