Curves & Motion · Superchallenge problem

A charged particle in a uniform magnetic field obeys $\mathbf v'(t) = \boldsymbol\omega\times\mathbf v(t)$ with $\boldsymbol\omega = (0, 0, 2)$, and its initial velocity is $\mathbf v(0) = (3, 0, 4)$. Find the radius of curvature of its path.