I followed the initial steps you did, but setting up the equation to take the derivative is what I don't understand.
I found a very similar answer to where you were headed, where they did show a few extra steps.
However I don't understand how they did the steps. Maybe this will make sense to you...
Thanks for your post!
My first thought was to do the dot product of the 2 velocity vectors V1 \cdot V2 and that's it.
The numbers didn't make any sense so I knew it was wrong.
Yes it would be very helpful to me if I understood the formulas and how they are derived.
But why do we have: \vec{A}: (2,8,8) \;x,y,z\text{ pos.}
The positions of the vectors may aid to solve the problem geometrically, but I'm
not sure if they are strictly needed to solve the problem. I think it depends
what method is used.
The closing velocity is how fast A is going towards B plus...