Two particles travel along the space curves
$ r_1 (t) = \langle t, t^2, t^3 \rangle $ $ r_2 (t) = \langle 1 + 2t, 1 + 6t, 1 + 14t \rangle $
Do the particles collide? Do their paths intersect?
does not collide, intersect at $(1,1,1)$ and $(2,4,8)$
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