Calculate \(\mathbf{T}_{u}, \mathbf{T}_{v}\), and \(\mathbf{N}(u, v)\) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point.

\(\Phi(u, v)=(2 u+v, u-4 v, 3 u) ; \quad u=1, \quad v=4\)