There are $2$ particles. One travels along the path $p_1(t) = \langle2.666 \cos(6.405t + 5.149) + 4.430, 2.666 \sin(6.405t + 5.149) − 3.610, 11.18t + 6.633 \rangle$ and the other along the path $p_2(t) = \langle 1.084t + 3.125, 3.096t − 5.332, −2.925t + 4.377 \rangle$ rsect at two points, one of which is a collision.
I have to find the point where the particles collide. I initially set the z components of each of the vectors equal to each other and solved for $t$ to get $-0.159943$. This value works out for each of the components, however, I'm not sure if I'm allowed to have a negative time. Is this the correct way to do this problem?
$t$ need not represent time, it is just a general parameter.
If it represent time, it means it doesn't collide after the reference time $0$ and it happens before that.