electromagnetism - $Etimes B$ drift of a single particle in vacuum with unifiorm $E$ and $B$

The force on a charged particle in electric field $E$ and magnetic field $B$ is given by:

$$\begin{equation} m \dot{v} = q ( E + v \times B) \end{equation}$$ Then, the $E \times B$ drift velocity $v_E$ of a single particle of mass $m$ and charge $q$ in a uniform magnetic field $B$ and a uniform electric field $E$ is given by $$\begin{equation} v_E= E \times B /B^2 \end{equation}$$ and if $E$ and $B$ are perpendicular, $v_E=E/B$.

How do I understand the fact that $v_E \propto 1/B$ ?

if $B \sim 0$, $V_E \sim \infty$, more than the velocity of light. Furthermore,it is also plausible that $V_E >> v_{th}$, the thermal velocity.