Lorentz transformation of the Electromagnetic field

Consider an inertial system $mathcal{O}$ and a Lorentz boosted system $mathcal{O}’$, moving with a velocity $vec{v}$ with respect to $mathcal{O}$. Then we have expressions for the electromagnetic fields as follows:
$$vec{B}=gammavec{B’}+frac{vec{v}}{v^2}(vec{v}cdotvec{B’})(1-gamma)+gammafrac{vec{v}}{c}timesvec{E’}$$
$$vec{E}=gammavec{E’}+frac{vec{v}}{v^2}(vec{v}cdotvec{E’})(1-gamma)-gammafrac{vec{v}}{c}timesvec{B’}
$$
Now, I want to find the condition that $vec{E’}$ and $vec{B’}$ have to satisfy such that there exists a $vec{v}$ such that $vec{E}=0$. I reckoned that the third term $vec{v}timesvec{B’}$ is perpendicular to the second term $vec{v}$, so those two cannot cancel each other. However, how can I formulate these conditions in terms of $vec{E’}$ and $vec{B’}$?