The electric and the magnetic fields associated with an electromagnetic wave propagating along the Z- axis, can be represented by

The electric field $\overrightarrow{E}$and magnetic fields $\overrightarrow{B}$are perpendicular to each other and also perpendicular to the direction of propagation of wave, so the direction of propagation of waves is the same as direction of $\left(\overrightarrow{E}\times \overrightarrow{B}\right)$

Now, given that an electromagnetic wave propagating along the Z- axis or $\hat{\mathrm{k}}$

Therefore, the $E=E_0\hat{\mathrm{i}} \text{and} B=B_0\hat{\mathrm{j}}$ because $\hat{\mathrm{i}}\times \hat{\mathrm{j}}=\hat{\mathrm{k}}$