A vector P is given by \({\rm{\vec P}} = {{\rm{x}}^3}{\rm{y}}{{\rm{\vec a}}_{\rm{x}}} - {{\rm{x}}^2}{{\rm{y}}^2}{{\rm{\vec a}}_{\rm{y}}} - {{\rm{x}}^2}{\rm{yz}}{{\rm{\vec a}}_{\rm{z}}}\) . Which one of the following statements is TRUE?
1
P is solenoidal, but not irrotational
2
P is irrotational, but not solenoidal
3
P is neither solenoidal nor irrotational
4
P is both solenoidal and irrotational