To solve this problem, we need to understand the properties of electromagnetic waves.$\\$For a plane electromagnetic wave propagating in the x-direction, the electric field $E \\$and the magnetic field $B$ are perpendicular to each other and also to the direction of propagation.$\\$Let's denote:$\\$• The direction of propagation is $\hat{i}. \\$• The electric field $E$ can be in the $\hat{j}$ or $\hat{k}$ direction, or a combination of both.$\\$• The magnetic field $B$ must be perpendicular to both the direction of propagation and $E. \\$Using the right-hand rule for electromagnetic waves:$\\$• If the wave is propagating in the $\hat{i}$ direction, and $E$ is in the $\hat{j}$ direction,$\\$ then $B$ must be in the $\hat{k}$ direction.$\\$• If $E$ is in the $\hat{k}$ direction, then $B$ must be in the $\hat{j}$ direction.$\\$Let's analyze the options:$\\$Option 1: $E = \hat{j} + \hat{k}, B = \hat{j} + \hat{k} \\$• Both $E$ and $B$ are not perpendicular to each other.$\\$Option 2: $E = -\hat{j} + \hat{k}, B = -\hat{j} - \hat{k} \\$• $E$ and $B$ are perpendicular to each other, and both are perpendicular to $\hat{i}. \\$Option 3: $E = \hat{j} + \hat{k}, B = -\hat{j} - \hat{k} \\$• Both $E$ and $B$ are not perpendicular to each other.$\\$Option 4: $E = -\hat{j} + \hat{k}, B = -\hat{j} + \hat{k} \\$• Both $E$ and $B$ are not perpendicular to each other.$\\$Therefore, the correct option is Option 2, where $E$ and $B$ are perpendicular to each other and $\\$to the direction of propagation.