A solid insulating sphere of radius \(R\) has a uniform positive volume charge density \(+\rho\). An off-center spherical cavity of radius \(b\) (where \(b < R/2\)) is scooped out from the interior of the sphere, such that its center is located at a fixed displacement vector \(\vec{d}\) from the center of the large sphere, with \(|\vec{d}| + b < R\). Which of the following statements correctly describes the electric field \(\vec{E}\) inside the cavity and provides the correct justification?