A 3 dimension vector problem with displacement. Attachments in PDF format.

A cosmic ray plows into Earth's upper atmosphere, liberating a shower of subatomic particles.  One of these particles moves downward 3.2 km, then undergoes a collision after which it moves 1.6 km at 27 deg. northward of the vertical.  It then undergoes another collision that sends it moving horizontally eastward for 2.1 km before it annihilates with another particle.  What is the magnitude of its displacement ?