A vector field $\vec{p}$ and a scalar field $r$ are given by
\[
\begin{aligned}
\vec{p} & =\left(2 x^{2}-3 x y+z^{2}\right) \hat{\imath}+\left(2 y^{2}-3 y z+x^{2}\right) \hat{\jmath}+\left(2 z^{2}-3 x z+x^{2}\right) \hat{k} \\
r & =6 x^{2}+4 y^{2}-z^{2}-9 x y z-2 x y+3 x z-y z
\end{aligned}
\]
Consider the statements $\mathrm{P}$ and $\mathrm{Q}$.
$\text{P}$: Curl of the gradient of the scalar field $r$ is a null vector.
$\text{Q}$: Divergence of curl of the vector field $\vec{p}$ is zero.
Which one of the following options is CORRECT?
- Both $\mathrm{P}$ and $\mathrm{Q}$ are FALSE
- $\text{P}$ is TRUE and $\text{Q}$ is FALSE
- $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE
- Both $\mathrm{P}$ and $\mathrm{Q}$ are TRUE