I need help with the following question about electromagnetic fields

Consider the electromagnetic field: (Assume that x x y = z) E = Eo cos(kz - wt) x B = Bo cos(kz - wt) y a) Show that there is no free charge in this electromagnetic field. b) Show that this electromagnetic field can satisfy all of Maxwell's equations with some constraints on Eo, Bo, k, w. c) Write down the equation of motion for an electric charge q in this electromagnetic field, assuming that the field created by q is negligible compared to E. and Bo