  In this paper, we investigate sufficient condition for the invariance of a
rectifying curve on a smooth surface immersed in Euclidean 3-space under
isometry by using Darboux frame $\left\lbrace T, P, U\right\rbrace$. Further,
we find the deviations of the position vector of a rectifying curve on the
smooth surface along any tangent vector $T = a\phi_u + b\phi_v$ with respect to
the isometry. We also find the deviations of the position vector of a
rectifying curve on the smooth surface along the unit normal $U$ to the surface
and along $P (= U \times T)$ with respect to the isometry.
