A vector \[\overrightarrow P \] is given by \[\overrightarrow P = {x^3}y{\overrightarrow a _x} - {x^2}{y^2}{\overrightarrow a _y} - {x^2}yz{\overrightarrow a _z}\]
Which of the following statements is TRUE?

A. \[\overrightarrow P \] is solenoidal, but not irrotational

B. \[\overrightarrow P \] is irrotational, but not solenoidal

C. \[\overrightarrow P \] is neither solenoidal nor irrotational

D. \[\overrightarrow P \] is both solenoidal and irrotational

Answer: Option A