\({\rm{\vec F}} = \left( {{{x}} + 3{{y}} - {{{c}}_1}{{z}}} \right){{\rm{\hat a}}_{\rm{x}}} + \left( {{{{c}}_2}{{x}} + 5{{z}}} \right){{\rm{\hat a}}_{\rm{y}}} + \left( {2{{x}} - {{{c}}_3}{{y}} + {{{c}}_4}{{z}}} \right){{\rm{\hat a}}_{\rm{z}}}\) is both irrotational and solenoidal. The value of c1 and c4 is
1
c1 = -1 and c4 = 2
2
c1 = -2 and c4 = -1
3
c1 = 3 and c4 = -5
4
c1 = -5 and c4 = 3