# What is the propagation direction of plane wave?

As far I know, plane wave equation is given by:
$$\vec{E}(\vec{r},t)=\vec{E_0} \cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm} \tag{1}$$ In some textbook propagation direction of $$(1)$$ is given as $$\vec{k}$$;
while in some other books, i found propagation direction of $$(1)$$ as $$-\vec{k}$$
so, can anyone tell me what is the propagation direction of $$(1)$$ and how can we determine it from $$(1)$$?

$$\vec E(\vec r,t)$$ is at a peak when $$e^{i(\vec k \cdot \vec r-\omega t)} = 1$$, and a minimum when it is $$-1$$. Maxima happen when $$i(\vec k \cdot \vec r-\omega t) = 0$$ or $$2 \pi i$$. It is at a minimum when the exponent is $$\pi i$$.
One peak is found where $$\vec k \cdot \vec r =\omega t$$. As t gets larger, the peak will move to where $$\vec k \cdot \vec r$$ is larger. To make the dot product larger, choose an $$\vec r$$ farther in the direction that $$\vec k$$ points.
That is to say, the wave will propagate in the direction that $$\vec k$$ points.