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Here we'll provide some guidance for solving those much less pleasant "multi-frame" problems that involve relative velocities, thanks to the fact the proper-velocities are not only synchrony free, but also behave the way you might expect 3-vectors to behave given that, after all, they also represent momentum per unit mass.
We use the familiar 3-vector form wAC = wAB*+wB*C, where e.g. wAC refers to the proper-velocity wAC ≡ δxAC/δτA of object A with respect to the map-frame of object C. However the asterisks are new.
In particular wAB* = wAB⊥wBC + γBCwAB||wBC has its reference metric changed (from B → C), while wB*C = γABwBC has only its time clock changed (from B → A).
Note in particular that unlike the low-speed case, wAC ≠ -wCA (even though their magnitudes are the same) when drawn from a third-frame perspective because the 2nd "reference frame" subscript in each case specifies a different definition of simultaneity. This result of shifting map-frames is referred to as "frame-shift" (Wigner) rotation from wAB+wBC toward the direction of the intermediate frame's proper-velocity wBC. It is clearly an artifact of viewpoint choice, because from the vantage point of both A and C, one can still say that wAC = -wCA!
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