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An electromagnetic wave in vacuum has the electric and magnetic field $\vec E$ and $\vec B$ , which are always perpendicular to each other. The direction of polarization is given by $\vec X$ and that of wave propagation by $\vec k$ . Then
$\overrightarrow {X\;} $ $॥ $ $\vec B$ and $\overrightarrow {\;k} $ ॥$\overrightarrow {\;B} $ $\times $ $\vec E$
$\overrightarrow {X\;} $ $॥ $ $\vec E $ and $\overrightarrow {\;k} $ ॥$\overrightarrow {\;E} $ $\times $ $\vec B$
$\overrightarrow{X\;} $ $॥ $ $\vec B$ and $\overrightarrow {\;k} $ ॥$\overrightarrow {\;E} $ $\times $ $\vec B$
$\overrightarrow {X\;} $ $॥ $ $\vec E$ and $\overrightarrow {\;k} $ ॥$\overrightarrow {\;B} $ $\times $ $\vec E$
Solution
Direction of polarization is parallel to magnetic field,
$\therefore \bar{X} \| \vec{E}$
And direction of wave propagation is parallel to $\vec{E} \times \vec{B}$ $\vec{k} \| \vec{E} \times \vec{B}$