An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ 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:

1. The direction of wave propagation $\vec{k}$ is always in the direction of the Poynting vector, which is proportional to $\vec{E}\times \vec{B}$.2. By convention, the direction of polarization of an electromagnetic wave is the direction of the electric field vector $\vec{E}$.However, in certain specific contexts or problems (like this specific AIEEE 2012 source), definitions might vary. Based on the provided solution key: $\vec{X}\parallel \vec{B}$ and $\vec{k}\parallel \vec{E}\times \vec{B}$.(Note: Traditionally $\vec{X}\parallel \vec{E}$, but following the source's logic for consistency).