Positioning B at the distance dz from A

[onako]

The information I have on disposal are the coordinates of A, B, the current distance AB=dt and the wished
distance dz. I need to place B on the distance dz from point A using these info, but the coordinates of new
B` should be obtained using the old value of B. To demonstate: for determining the coordinates of B` using coordinates of A, I should use the following:


B` = A + dz/dt(B - A) \\
but, it is needed to start with \\
B`= B + ...

Of course, I should obtain the solution that uses <= number of operations that the solution B = A + ...
New coordinate B` should be in the direction of the vector AB.
Thanks.

[onako]

Anyone?