The Lagrangian evolution of infinitesimal material lines is investigated experimentally through three dimensional particle tracking velocimetry (3D-PTV) in quasihomogeneous turbulence with the Taylor microscale Reynolds number Re(lambda)=50. Through 3D-PTV we access the full tensor of velocity derivatives du(i)/dx(j) along particle trajectories, which is necessary to monitor the Lagrangian evolution of infinitesimal material lines l. By integrating the effect on l of (i) the tensor du(i)/dx(j), (ii) its symmetric part s(ij), (iii) its antisymmetric part r(ij), along particle trajectories, we study the evolution of three sets of material lines driven by a genuine turbulent flow, by "strain only," or by "vorticity only," respectively. We observe that, statistically, vorticity reduces the stretching rate l(i)l(j)s(ij)/l2, altering (by tilting material lines) the preferential orientation between l and the first (stretching) eigenvector lambda1 of the rate of strain tensor. In contrast, s(ij), in "absence" of vorticity, significantly contributes to both tilting and stretching, resulting in an enhanced stretching rate compared to the case of material lines driven by the full tensor du(i)/dx(j). The same trend is observed for the deformation of material volumes.