 Solution

The phase $kz-\omega t$ describes propagation along $+z$. With $\psi =kz-\omega t$, the vacuum plane electromagnetic wave hasThus $B_x=-3A\sin \psi /c$, $B_y=2A\sin \psi /c$, and $B_z=0$. The field amplitudes are $E_0=\sqrt{13}|A|$ and $B_0=\sqrt{13}|A|/c$, givingThe instantaneous magnitude ratio also equals $c$ wherever the fields are nonzero; at a node both vanish together. Their Poynting vector points along $+z$, checking the relative component signs.