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[tex] \mathbf{E}(x,y,z)= \frac{1}{4\pi\epsilon_0 } \int \frac{\rho(x',y',z')\boldsymbol{\hat r} dx'dy'dz'}{r^{2}} [/tex].

It's stated that (x,y,z) is fixed while we let the variables x', y' and z' range over the domain of integration. What puzzles me is that radial unit vector, which is supposed to point from (x', y', z') to (x,y,z), making the integrand a vector valued function.

What am I missing?