A rectifying curve γ in the Euclidean 3-space E 3 is defined as a space curve whose position vector always lies in its rectifying plane (i.e., the plane spanned by the unit tangent vector field T γ and the unit binormal vector field B γ of the curve γ), and an f -rectifying curve γ in the Euclidean 3-space E 3 is defined as a space curve whose f -position vector γ f , defined by γ f (s) = f (s)dγ, always lies in its rectifying plane, where f is a nowhere vanishing real-valued integrable

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... in arc-length parameter s of the curve γ. In this paper, we introduce the notion of f -rectifying curves which are null (lightlike) in the Minkowski 3-space E 3 1 . Our main aim is to characterize and classify such null (lightlike) f -rectifying curves having spacelike or timelike rectifying plane in the Minkowski 3-Space E 3 1 .