Chapter 12.2, Problem 52ES

Show that the graphs of ${\text{r}}_1\left(t\right){\text{ and r}}_2\left(t\right)$ intersect at the point P. Find, to the nearest degree, the acute angle between the tangent lines to the graphs of ${\text{r}}_1\left(t\right){\text{ and r}}_2\left(t\right)$ at the point P.

$\begin{array}{l}{\text{r}}_1\left(t\right)=2e^{-t}\text{i}+\cos t\text{j}+\left(t^2+3\right)\text{k}\\ {\text{r}}_2\left(t\right)=\left(1-t\right)\text{i}+t^2\text{j}+\left(t^3+4\right)\text{k};P\left(2,1,3\right)\end{array}$