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Q.
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?
$(\vec{ E } \times \vec{ B })$ gives the direction of propagation
$\vec{ E }=-\hat{ j }+\hat{ k }, \vec{ B }=-\hat{ j }-\hat{ k }$
$\vec{E} \times \vec{B}=\begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\ 0 & -1 & 1 \\ 0 & -1 & -1\end{vmatrix}=2 \hat{i}$
Also $\vec{E} \cdot \vec{B}=(-\hat{j}+\hat{k})(-\hat{j}-\hat{k})=0$