If two objects travel through space along two different curves, it is often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) Their paths might intersect, but we need to know whether the objects are in the same position at the same time. Suppose two particles travel along the following space curves. r 1
(t)=⟨t,t 2
,t 3
⟩,r 2
(t)=⟨1+6t,1+30t,1+126t⟩ for t≥0 Find the points at which their paths intersect. (If an answer does not exist, enter DNE.) smaller x-value (x,y,z)=(1,1,1
(x,y,z)=(
Find the time(s) when the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t=