Two particles travel along the space curves r1t t t2 t3

Question

Two particles travel along the space curves

r₁(t) = (t, t², t³)

r₂(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) = ? (smaller x-value)

(x, y, z) =? (larger x-value)

Find the points where the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t =?