Two particles travel along the space curves
$$r_1(t) = (t, t^2, t^3)$$
$$r_2(t) = (1+2t, 1+6t, 1+14t)$$
Find the points at which their paths intersect. (If an answer does not exist, enter DNE.)
$$(x, y, z) = (1, 1, 1)$$
$$(x, y, z) =$$
(smaller x-value)
(larger x-value)
Find the time(s) when the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
$$t = DNE$$