An irrotational vector field has zero curl. For the given components, the curl is $$\nabla\times\mathbf F=(2-k_3)\hat a_x-k_1\hat a_y+(k_2-3)\hat a_z.$$ Each coefficient must vanish independently. Hence $k_3=2$, $k_1=0$ and $k_2=3$.
In the requested order the triple is **(0,3,2), B**.
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