A plane electromagnetic wave in a vacuum has electric field

$$\mathbf{E}=\left(E_{0} \sin k(z-c t), 0,0\right)$$

What are the wavevector, polarization vector and speed of the wave? Using Maxwell's equations, find the magnetic field B. Assuming the scalar potential vanishes, find a possible vector potential $\mathbf{A}$ for this wave, and verify that it gives the correct $\mathbf{E}$ and $\mathbf{B}$.