Particle collision and path intersection

Given two parametric equations how can we tell if the paths that they trace out over time intersect (or overlap) and whether or not the particles moving along those paths collide?
Source files here: sites.google.c...

[@gonderage]

yo thanks, diggity dawg! I had no idea how to solve this problem, and neither my textbook nor my professor went over this question or did a similar problem to prepare me for it.

[@mathteacher1729]

You're welcome! So glad people are still finding my videos after all these years.

[@lleytonmorris6305]

I am doing specialist mathematics and I came across a similar question and could not understand how this worked since the original condition was that t > 0 and it confused my fellow classmates as to how saying s = t didn't make s have to be greater than 0 also, but I comfortably understand that by making it s, it is in a separate timeline and the time can be treated like a vector quantity and placed even in negative time zones. So I am Really grateful for this video

[@zachhong554]

Thanks man this helped me figure out the difference between collision and crossing of paths

[@AllRounderAndyy]

how comes you didn't use the z component when determining if they intersected?

[@wanderer3612]

The values of the question seems familiar xd

[@PiscesWaffles]

Thanks Joe!

[@ashleycarman8031]

This was so helpful! Curse Michigan Math, and thank you!!

[@mathteacher1729]

Thank you! I'm so glad my old math videos are still helpful. :)

[@psicojorge]

Great explanation, many thanks!

[@davidjiang1437]

you are messing up the idea of intersect and collide? you call collide as intersect for several times

[@heavymetalman2]

good shit

[@FcBarcelonaKid]

Thank you!

[@jon7222]

Thanks this helped a lot!

[@jeffma7202]

Helpful! tks

[@seangiomi6126]

joe i love you bro preesh

[@heavymetalman2]

what program did you use to model the motion?

[@mathteacher1729]

I used dpgraph. The link in my info was broken but I fixed it. The source files are available for download at the bottom of the page now.