The three-dimensional flow of a hybrid nanofluid over a stretching/shrinking sheet including copper and alumina nanoparticles in ethylene glycol has been investigated under the influence of magnetic field, thermal radiation, joule heating, convective conditions, and slip boundary conditions. Hybrid nanofluids disperse two distinct nanoparticles in a fluid, providing better heat conductivity for industrial applications. Using the bvp4c technique, non-linear partial differential equations are transformed into non-linear ordinary differential equations with similarity variables. Velocity profile declines with higher magnetic, suction, and slip parameter values, while sheet temperature profile growths with Biot, Eckert, and radiative parameters. The study discovers that a stronger magnetic force enhances temperature across a stretched sheet but has the reverse impact on a shrinking sheet. The novelty lies in using a three-dimensional model for this investigation, providing more accurate and realistic representations of fluid flow and heat transport compared to conventional two-dimensional models. In contrast to the earlier experiment, ethylene glycol, the base fluid, and three-dimensional flow are both taken into account, along with alumina and copper nanoparticles scattered in it. Quantitative analysis of the results demonstrates that in hybrid nanofluids, a higher Biot number and Reynolds number result in a faster rate of heat transfer.