An electric field has a potential of $V(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} \mathrm{~V}$. A charge of $1$ coulomb placed at $(\hat{\imath}+\hat{\jmath}+\hat{k})$ experiences a force of
$$\vec{F}=(a \hat{\imath}+b \hat{\jmath}+c \hat{k}) \mathrm{N}$$
The values of $(a, b, c)$ are $\_\_\_\_$.
- $a=\dfrac{1}{\sqrt{3}}, b=\dfrac{1}{\sqrt{3}}, c=\dfrac{1}{\sqrt{3}}$
- $a=\dfrac{1}{3}, b=\dfrac{1}{3}, c=\dfrac{1}{3}$
- $a=0, b=1, c=\dfrac{1}{\sqrt{3}}$
- $a=0, b=1, c=\dfrac{1}{3}$
