The following comes from Landau's Mechanics, pages 97 - 98. For a particle in a rigid body, v = V + W x r -- (1) where for some origin O of the moving body measured in the "fixed" system of co-ordinates, v = particle's velocity in body in the "fixed" system, V = velocity of O in "fixed" system , W is the body's angular velocity in *fixed system", x is a cross product and r the particle's radial vector within body measured from O. For another origin, O' distance a from O, r = r' + a, and substituting in (1) gives: v = V + W x a + W x r'. The definition of V' and W' shows that v = V' + W' x r' and so V' = V + W x a, W' = W -- (2) He then says that the first part of (2) shows that if V and W are perpendicular for a choice of origin O, then V' and W' are also perpendicular for O'. Why? Thanks in advance.