If two objects travel through space along two different curves, it's often important to know whether they will collide. $($Will a missile hit its moving target? Will two alrcraft collide?$)$ The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions

$r_1(t)=($:$t^2,9t-14,t^2$:$),r_2(t)=($:$16t-63,t^2,8t-7$:$)$

for $t0.$ Find the values of $t$ at which the particles collide. $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$t=$