Plane and spherical electromagnetic waves

According to my physics book, the component of the magnetic field (in the y direction) of an electromagnetic wave can be described by the following function:

(IMPORTANT: take only the real part of the complex number $e^{iω(t-(x/c))}$ )

$$B_y(x,t) = B_0 , e^{iω(t-(x/c))}$$

The same can be done with the electric field component in the z direction:

$$E_z(x,t) = E_0 ,e^{iω(t-(x/c))}$$

My book states that $-E_0/c = B_0$. My first question is: shall I assume that $E_0$ and $B_0$ are respectively the component of the electric field in the z direction and the component of the magnetic field in the y direction (vector quantities)?

The same can question could be asked about the spherical waves. According to my book, the electric field $E(r,t) = frac{E_0}{r} sin(kr-ωt)$ is a spherical wave. Anyway I am not sure if here $E_0$ is a component of the electric field or not. But I know that $E(r,t)$ is the component of the electric field in spherical polar coordinates.