In a region the potential is represented by V(x, y, z) = 6x - 8xy -...

Potential in the space varies as ${V}_{\left(x, y, z\right)} = 6x - 8xy - 8y + 6yz$.

Electric field is given by,
${E}_{x} = - \dfrac{∂ V}{∂ x} = - 6 + 8y$
${E}_{y} = - \dfrac{∂ V}{∂ y} = 8x + 8 - 6z$
${E}_{z} = - \dfrac{∂ V}{∂ z} = - 6y$
\overset{\to}{E} = \left(- 6 + 8y\right)\overset{^}{i} + \left(8x + 8 - 6z\right)\overset{^}{j} - 6y\overset{^}{k}

Putting the value of the position we get,
{\overset{\to}{E}}_{\left(1, 1, 1\right)} = 2\overset{^}{i} + 10\overset{^}{j} - 6\overset{^}{k}

Magnitude is given by,
\left|\overset{\to}{E}\right| = 2\sqrt{35}N{C}^{- 1}$</p><p>Force on the charge is given by,<br />$F = qE = 2 \times 2\sqrt{35} = 4\sqrt{35}N