Final answer:
The direction of a plane electromagnetic wave traveling in the positive x-axis is such that its electric field oscillates along the z-axis and its magnetic field oscillates along the negative y-axis, according to the right-hand rule.
Step-by-step explanation:
The direction of a plane electromagnetic wave traveling in the positive direction of an x-axis can be understood using the right-hand rule, where the thumb points in the direction of the current (or the direction of the wave vector for electromagnetic waves), and the fingers curl in the direction of the electric field. The palm then points in the direction of the magnetic field. In the question, it is assumed that the electric field E is oscillating along the z-axis and the magnetic field B is oscillating along the x-axis.
According to the right-hand rule, for a wave traveling along the positive x-axis, the electric field would be in the direction of the positive z-axis, and the magnetic field would be in the direction of the negative y-axis. Thus, the plane electromagnetic wave would be traveling along the positive x-axis, as stated in the question. This is due to the fact that electromagnetic waves have their electric and magnetic fields perpendicular to each other and also perpendicular to the direction of propagation.