Question

help! Q on the comment! Medal and fan available!

Answer 1

two particles travel in space, give by the following vectors\[r(t)=(t,t ^{2},t ^{3}\]

Answer 2

\[r _{2}(t)=\left( 1+2t, 1+6t, 1+14t \right)\]

Answer 3

do they collide?

Answer 4

do the paths intersect?

Answer 5

I know they don't collide because there is no valid solution for t

Answer 6

but how do I check for inersection

Answer 7

the components of position vector will be equal when they intersect

Answer 8

if there is no such t value, that means the path are skew

Answer 9

so hese two are the same thing?

Answer 10

I mean I find if they collide by equating components

Answer 11

yes i would do the same

Answer 12

t = 1+2t

t = -1

but this doesn't produce same components for y,z
so the paths never collide

Answer 13

*particles never collide

Answer 14

ok thx

Answer 15

there is a difference between collision and intersection of paths

Answer 16

yes I thought so, but what's that

Answer 17

if you are walking behind me at same speed as mine,
our both paths intersect at infinitely many points, but we never collide because our speeds are same