If electric \( \vec{E}(r,t) \) and magnetic \( \vec{B}(r,t) \) fields are defined as
\[
\vec{E}(r,t) = \vec{E}_0 e^{i(k \cdot r - \omega t)} \hat{n}, \quad \vec{B}(r,t) = \frac{1}{c} \hat{k} \times \vec{E}(r,t)
\]
where \( k \) is the propagation vector and \( \hat{n} \) is the polarization vector. E and B are transverse in nature, if they satisfy which of the following conditions?