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This question already has an answer here:

How are kx-wt and kx+wt in terms of the direction of the wave. I have been stuck at this or an hour, still can not find a definitive answer.

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marked as duplicate by Rob Jeffries, John Rennie electromagnetism Apr 28 at 11:11

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Generally, the phase of the eletromagnetic wave is going to be $\phi = \vec k \cdot \vec r \pm wt$; from this expression, we can interpret the direction of the wave. Take a fixed time, then look for direction of the $\delta \vec r$ that maximizes your $\delta \phi$. That's the direction of propagation of the wave. It will be parallel to $\vec k$.

The "sense" of propagation in the direction of $\vec k$ is determined by the sign on $wt$; If your $\delta \vec r$ has the same direction and sense of $\vec k$, then, to maintain the phase, your $\pm w\delta t$ should be negative. That means a wave going "forward" on the sense of the propagation has a phase $\phi = \vec k \cdot \vec r - wt$, and a wave going "backwards" has a phase $\phi = \vec k \cdot \vec r + wt$.

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