Section 13.1: Vector Functions and Space Curves

Two particles travel along the space curves \(\mathbf{r}_1(t) = \langle t, t^2, t^3 \rangle\) \(\mathbf{r}_2(t) = \langle 1+2t, 1+6t, 1+14t \rangle\) Do the particles collide? Do their paths intersect?