Solution
= Solution
In <Minkowski spacetime> with metric $-dt^2+dx^2+dy^2+dz^2$, take
$$
\boxed{\gamma(t)=(t,\cos t,\sin t,0).}
$$
Its <tangent vector> is $(1,-\sin t,\cos t,0)$, with <metric tensor> square $-1+\sin^2t+\cos^2t=0$. Its <acceleration> is $(0,-\cos t,-\sin t,0)$, nonzero and not proportional to the tangent because its time component is zero. Thus it is a regular <null curve> which is \b[not a <geodesic> under any reparametrization].