Show that the transformation equations derived in Exercise 6.5 can be written as
E∥′=E∥,E⊥′=γ(E⊥+v×B⊥),B∥′=B∥,B⊥′=γ(B⊥−c21v×E⊥),
where v=(v,0,0), and E∥ and E⊥ denote the projections of E parallel and orthogonal to v respectively (and similarly for B). Explain why these equations must hold for a Lorentz boost v in an arbitrary direction with respect to the axes of S.