Suppose that a particle has threevector velocity v as seen from the S system and v as seen from S...

Suppose that a
particle has threevector velocity v as seen from the S system and v as seen
from S. Assume S and S related by a general boost parameterized by the
threevector velocity V between the systems.

(a) Show that

where v = Vˆ Vˆ
· v is the component of v parallel to V and v⊥ = v − v is the component perpendicular to
V, with similar definitions in the S system.