In an electromagnetic wave, the electric field vector and magnetic field vector are given as $\mathrm{E}={\mathrm{E}}_0\hat{\mathrm{i}}\text{ and }\mathrm{B}={\mathrm{B}}_0\hat{\mathrm{k}}$, respectively. The direction of propagation of electromagnetic wave is along

In an electromagnetic wave, the electric field vector and magnetic field vector are given as

$\mathrm{E}={\mathrm{E}}_0\hat{\mathrm{i}}$              ...(i)

and $\mathrm{B}={\mathrm{B}}_0\hat{\mathrm{k}}$     ...(ii)

$\because$ Direction of electromagnetic wave is given by direction of $\mathrm{E}\times \mathrm{B}$ because it is perpendicular to both E and B vectors.

So, unit vector in direction of $\mathrm{E}\times \mathrm{B}$ will be

$=\frac{\overrightarrow{\mathrm{E}}\times \overrightarrow{\mathrm{B}}}{|\overrightarrow{\mathrm{E}}\times \overrightarrow{\mathrm{B}}|}$                              ...(iii)

From Eqs. (i), (ii) and (iii), we get

$\frac{{\mathrm{E}}_0\hat{\mathrm{i}}\times {\mathrm{B}}_0\hat{\mathrm{k}}}{{\mathrm{E}}_0{\mathrm{B}}_0\sin {90}^{\circ }}=\hat{\mathrm{i}}\times \hat{\mathrm{k}}=-\hat{\mathrm{j}}$