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A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x – x^2y^2\overrightarrow{a}_y – x^2 yz \overrightarrow{a}_z$. Which one of the statements is TRUE?

  1. $\overrightarrow{P}$ is solenoidal, but not irrotational
  2. $\overrightarrow{P}$ is irrotational, but not solenoidal
  3. $\overrightarrow{P}$ is neither solenoidal, nor irrotational
  4. $\overrightarrow{P}$ is both solenoidal and irrotational
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