d
Here, \(V(x, y, z)=6 x-8 x y-8 y+6 y z\)

The \(x, y\) and \(z\) components of electric field are

\(E_{x} =-\frac{\partial V}{\partial x}=-\frac{\partial}{\partial x}(6 x-8 x y-8 y+6 y z)\)

\(=-(6-8 y)=-6+8 y\)

\(E_{y} =-\frac{\partial V}{\partial y}=-\frac{\partial}{\partial y}(6 x-8 x y-8 y+6 y z)\)

\(=-(-8 x-8+6 z)=8 x+8-6 z\)

\(E_{z} =-\frac{\partial V}{\partial z}=-\frac{\partial}{\partial z}(6 x-8 x y-8 y+6 y z)=-6 y \)

\(\vec{E} =E_{x} \hat{i}+E_{y} \hat{j}+E_{z} \hat{k}\)

\(=(-6+8 y) \hat{i}+(8 x+8-6 z) \hat{j}-6 y \hat{k}\)

At point \((1,1,1)\)

\(\bar{E}=(-6+8) \hat{i}+(8+8-6) \hat{j}-6 \hat{k}=2 \hat{i}+10 \hat{j}-6 \hat{k}\)

The magnitude of electric field \(\vec{E}\) is

\(\vec{E}=\sqrt{E_{x}^{2}+E_{y}^{2}+E_{z}^{2}}=\sqrt{(2)^{2}+(10)^{2}+(-6)^{2}}\)

\(=\sqrt{140}=2 \sqrt{35} \,{N} {C}^{-1}\)

Electric force experienced by the charge \(F=q E=2 \mathrm{C} \times 2 \sqrt{35} \mathrm{\,NC}^{-1}=4 \sqrt{35}\mathrm{\,N}\)