Question

Find the angle between the two space curves below at their point of intersection. r1(t) = <3t-1, t^(2) +1, square root(t+2)> r2(t)=<2t^(2)+3, 1-4t, t+3>

Answer 1

Notice
\[
\text{r2}(-1)=\text{r1}(2)=\{5,5,2\}\]

Answer 2

So (5,5,2) is where they intersect

Answer 3

Use the formula
\[
\cos(\theta) = \frac{\vec{x}\cdot \vec{y}}{||\vec{x}|| \ ||\vec{y}||}
\] where \[
\vec x=r1(2)\\
\vec y=r2(-1)

\]

Answer 4

don't you want the angle between the tangent vectors?