Chapter 13.1, Problem 36E

To determine

Which of the following statements are true?

(a) If ${\overrightarrow{r}}_1\left(t\right)\text{ and }{\overrightarrow{r}}_2\left(t\right)$ intersect, then they collide.

(b) If ${\overrightarrow{r}}_1\left(t\right)\text{ and }{\overrightarrow{r}}_2\left(t\right)$ collide then they intersect.

(c) Intersection depends only on the underlying curves traced by ${\overrightarrow{r}}_1$ and ${\overrightarrow{r}}_2$ but collision depends on the actual parameterizations.