If `vec(E)` and `vec(B)` represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of electromagnetic wave is along

Options

A. `vec`
B. `vec(B)`
C. `vec(B) xx vec(E)`
D. `vec(E) xx vec(B)`

Explanation

To determine the direction of propagation of an electromagnetic wave given the electric field vector \(\vec{E}\) and the magnetic field vector \(\vec{B}\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**: In an electromagnetic wave, the electric field vector \(\vec{E}\), the magnetic field vector \(\vec{B}\), and the direction of propagation \(\vec{C}\) are mutually perpendicular to each other. This means that the angle between any two of these vectors is 90 degrees.

2. **Using the Right-Hand Rule**: To find the direction of propagation, we can use the right-hand rule. If you point your right thumb in the direction of \(\vec{E}\) and your fingers in the direction of \(\vec{B}\), your palm will face in the direction of the wave's propagation \(\vec{C}\).

3. **Cross Product**: The direction of propagation can be mathematically represented as \(\vec{C} = \vec{E} \times \vec{B}\). This means that the direction of the wave is given by the cross product of the electric field and the magnetic field vectors.

4. **Graphical Representation**: If we visualize this in a 3D coordinate system:
- Let’s assume \(\vec{E}\) is along the x-axis.
- Let’s assume \(\vec{B}\) is along the y-axis.
- According to the right-hand rule, the direction of propagation \(\vec{C}\) will be along the z-axis.

5. **Conclusion**: Therefore, the direction of propagation of the electromagnetic wave is given by the vector \(\vec{C}\) which is perpendicular to both \(\vec{E}\) and \(\vec{B}\). In this case, if \(\vec{E}\) is along the x-axis and \(\vec{B}\) is along the y-axis, then the direction of propagation \(\vec{C}\) is along the z-axis.

### Final Answer:
The direction of propagation of the electromagnetic wave is along \(\vec{E} \times \vec{B}\).

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