In an electromagnetic wave, the electric field vector and magnetic field vector are given as $$\vec{E} = E_0\hat{i}$$ and $$\vec{B} = B_0\hat{k}$$, respectively. The direction of propagation of electromagnetic wave is along:

The direction of propagation of an electromagnetic wave is given by the cross product of the electric field vector and the magnetic field vector, i.e., the direction of $$\vec{E} \times \vec{B}$$.

Given $$\vec{E} = E_0\hat{i}$$ and $$\vec{B} = B_0\hat{k}$$, we compute:

$$\vec{E} \times \vec{B} = E_0 B_0 (\hat{i} \times \hat{k})$$

Using the right-hand rule for unit vectors: $$\hat{i} \times \hat{k} = -\hat{j}$$

Therefore, $$\vec{E} \times \vec{B} = E_0 B_0 (-\hat{j})$$

The direction of propagation of the electromagnetic wave is along $$(-\hat{j})$$.