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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 $\text{x, y and z}$

directions, respectively. The values of constants $k_{1}, k_{2},k_{3}$ are given by:

  1. $k_{1}=3, k_{2}=3,k_{3}=7$
  2. $k_{1}=3, k_{2}=8,k_{3}=5$
  3. $k_{1}=4, k_{2}=5,k_{3}=3$
  4. $k_{1}=0, k_{2}=0,k_{3}=0$
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