c
Given, \(V=6 x y-y+2 y z\)

\(\vec{E}=\left[\frac{\partial V}{\partial x} \hat{i}+\frac{\partial V}{\partial y} \hat{j}+\frac{\partial V}{\partial z} \hat{k}\right]\)

\(\vec{E}=-\left\{\frac{\partial}{\partial x}[6 x y-y+2 y z] \hat{i}+\frac{\partial}{\partial y}[6 x y-y+2 y z] \hat{j}\right.\)

\(\left.+\frac{\partial}{d z}[6 x y-y+2 y z) \hat{k}\right\}\)

\(=-\{(6 y) \hat{i}+(6 x-1+2 z) \hat{j}+(2 y) \hat{k}\}\)

\(\vec{E}_{1,1,0}=-\{(6 x 1) \hat{i}+(6 \times 1-1+2 \times 0) \hat{j}+(2 \times 1) \hat{k}]\)

\(=-(6 \hat{i}+5 \hat{j}+2 \hat{k})\)