An e.m. wave travels in vacuum along z direction:
`vecE=(E_1hati+E_2hatj)cos (kz-omega)`. Choose the correct option from the following :

Options

A. The associated magnetic field is given as `overline(B) = (1)/(C ) (E_(1) hat(i) + E_(2) hat(j)) cos (kz - omega t)`
B. The associated magnetic field is given as `overline(B) = (1)/(C ) (E_(1) hat(i) - E_(2) hat(j)) cos (kz - omega t)`
C. The given electromagnetic field is circularly polarised
D. The given electromagnetic field is not plane polarised

Explanation

To solve the problem, we need to analyze the given electric field vector of the electromagnetic wave and determine the correct options based on its characteristics.

### Step-by-Step Solution:

1. **Identify the Electric Field Vector**:
The electric field vector is given by:
\[ \vec{E} = (E_1 \hat{i} + E_2 \hat{j}) \cos(kz - \omega t) \]
This indicates that the electric field has components in both the x-direction (i) and the y-direction (j).

2. **Direction of Propagation**:
The wave is traveling in the z-direction, as indicated by the argument of the cosine function, which contains \( kz - \omega t \). This means the wave propagates along the z-axis.

3. **Determine the Magnetic Field Vector**:
According to electromagnetic wave theory, the relationship between the electric field \( \vec{E} \) and the magnetic field \( \vec{B} \) in a vacuum is given by:
\[ \vec{B} = \frac{1}{c} \vec{E} \]
where \( c \) is the speed of light. Thus, we can express the magnetic field vector as:
\[ \vec{B} = \frac{1}{c} (E_1 \hat{i} + E_2 \hat{j}) \cos(kz - \omega t) \]

4. **Check for Polarization**:
The electric field vector has components in the x and y directions, which means it is oscillating in a plane. This indicates that the wave is plane-polarized.

5. **Evaluate the Options**:
- **Option A**: Since \( \vec{B} = \frac{1}{c} \vec{E} \), this option is correct.
- **Option B**: This option has a negative sign, which is incorrect.
- **Option C**: It states that the wave is circularly polarized, which is incorrect because the electric field oscillates in a plane.
- **Option D**: This option states that the electromagnetic field is not plane polarized, which is also incorrect.

### Conclusion:
The only correct option is **Option A**. The wave is indeed plane polarized as it has electric field components in the x and y directions while propagating in the z direction.