An electric dipole with dipole moment \(p=4 \times 10^{-5} \mathrm{C}\)-m sets up an electric field (in newtons per coulomb)

\[
\mathbf{F}(x, y, z)=\frac{k p}{r^{5}}\left\langle 3 x z, 3 y z, 2 z^{2}-x^{2}-y^{2}ightangle
\]

where \(r=\left(x^{2}+y^{2}+z^{2}ight)^{1 / 2}\) with distance in meters and \(k=8.99 \times 10^{9}\) with units \(\mathrm{N}-\mathrm{m}^{2} / \mathrm{C}^{2}\). Calculate the work against \(\mathbf{F}\) required to move a particle of charge \(q=0.01 \mathrm{C}\) from \((1,-5,0)\) to \((3,4,4)\). Note: The force on \(q\) is \(q \mathbf{F}\) newtons.