The vector function expressed by
$$F=a_{x}\left ( 5y-k_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y-4x\right )$$
represents a conservative field, where $a_{x}, a_{y},a_{z}$ are unit vectors along $x, y$ and $z$ directions, respectively. The values of constants $k_{1}, k_{2},k_{3}$ are given by:
- $k_{1}=3, k_{2}=3,k_{3}=7$
- $k_{1}=3, k_{2}=8,k_{3}=5$
- $k_{1}=4, k_{2}=5,k_{3}=3$
- $k_{1}=0, k_{2}=0,k_{3}=0$