$A$ monochromatic beam of light has a frequency $v = \frac{3}{2\pi} \times 10^{12} \, Hz$ and is propagating along the direction $\vec{n} = \frac{\hat{i} + \hat{j}}{\sqrt{2}}$. It is polarized along the $\hat{k}$ direction. The acceptable form for the magnetic field $\vec{B}$ is:

• A
  $\frac{E_0}{c} \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right) \cos \left[ 10^4 \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} - (3 \times 10^{12})t \right]$
• B
  $\frac{E_0}{c} \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right) \cos \left[ 10^4 \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} - (3 \times 10^{12})t \right]$
• C
  $\frac{E_0}{c} \hat{k} \cos \left[ 10^4 \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} + (3 \times 10^{12})t \right]$
• D
  $\frac{E_0}{c} \frac{(\hat{i} + \hat{j} + \hat{k})}{\sqrt{3}} \cos \left[ 10^4 \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} + (3 \times 10^{12})t \right]$