Answer
$v_{avg} = -0.7i + 1.4j -0.4k $
Work Step by Step
The initial position of the ion is $ r = 5i - 6j + 2k $ and the final position is $ r = -2i + 8j - 2k $. Velocity is defined as $\frac{\Delta x}{\Delta t} $ so we need to take the final position and subtract the initial position to find the change in x
$\Delta x $ = (-2 -5) i + (8- -6)j + (-2 -2)k = -7i + 14j -4k $
Since this occurred over 10s, we divide the vector by 10 and get
$ v = -7/10 i + 14/10 j - 4/10k = -0.7i + 1.4j -0.4k $
