An ion's position vector is initially r = 8.0 i - 4.0 j + 3.0 k, and 8.0 s later it is r = 4.0 i + 8.0 j - 6.0 k, all in meters. what was its vavg during the 8.0 s?

The average velocity = Displacement between two points/ Time taken for that displacement

In this case An ion's position vector is initially r = 8.0 i - 4.0 j + 3.0 k, and 8.0 s later it is r = 4.0 i + 8.0 j - 6.0 k

So, displacement = 4.0 i + 8.0 j - 6.0 k - (8.0 i - 4.0 j + 3.0 k)

                             = -4.0 i + 12.0 j - 9.0 k

So velocity, V = (-4.0 i + 12.0 j - 9.0 k)/8

                      = -0.5 i + 1.5 j - 1.125 k

So average velocity during 8 seconds = -0.5 i + 1.5 j - 1.125 k

i would think it's food chain