For a plane electromagnetic wave propagating in $x$-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively ?
Answer: (C) $-\hat{j} + \hat{k},\ -\hat{j} - \hat{k}$
$\vec{E}$ and $\vec{B}$ must be perpendicular to each other, and $\vec{E} \times \vec{B}$ must point along $+\hat{i}$.
Options (1), (2) and (4) have $\vec{E}$ parallel or antiparallel to $\vec{B}$, so they are ruled out.
Option (3): $(-\hat{j} + \hat{k})\cdot(-\hat{j} - \hat{k}) = 1 - 1 = 0$, so they are perpendicular. And
$$(-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = \hat{j}\times\hat{k} - \hat{k}\times\hat{j} = \hat{i} + \hat{i} = 2\hat{i}$$
which is along $+x$.
Solution by Sreeraj P, M.Sc Physics