Two particles are traveling through space. At time $t$ the first particle is at the point $$(1 + 3 t, -3 - 2 t, 3 + 2 t)$$ and the second particle is at $$(-1 + t, -2 - t, 4 + 3 t)$$

Describe the two paths in words. Then determine if the two particles collide, cross, or neither cross nor collide to fill in the following.

We see that ? the paths cross, and the particles collide there the paths of the particles cross, but with no collision neither of these is true .

If they collide or their paths cross, indicate where (if neither is true, enter none).
A collision or crossing occurs at $(x,y,z) =$ .