you could do what this anon was saying: >>10995190
So the way you would do this:
since it is symmetric, the dot product doesn't change it's angle no matter how far apart the two points are moved
so when you maximize "d", you maximize "m".
The sphere has a radius of 2, thus the largest you can make "d" is 4
so it should be
of course you're just assuming a symmetrical answer there. I'm sure you can reason it out though.
One way you could "prove" the symmetric answer is correct is to do this:
then say that
and this is true when
There, that should be sufficient.