In a region of space, the three-dimensional electric potential is given by \(V(x,y,z) = Cxyz\), where \(C\) is a positive constant. Which of the following correctly identifies the electric field vector \(\vec{E}(x,y,z)\) and the set of points where \(\vec{E}\) is perpendicular to the position vector \(\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}\)?