The curl of the gradient of the scalar field defined by $V = 2 x^{2} y + 3 y^{2} z + 4 z^{2} x$ is

4 x y a_{x} + 6 y z a_{y} + 8 z x a_{z}

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4 a_{x} + 6 a_{y} + 8 a_{z}

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(4 x y + 4 z^{2}) a_{x} + (2 x^{2} + 6 y z) a_{y} + (3 y^{2} + 8 z x) a_{z}

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Solution

The correct option is D $0$
$V = 2 x^{2} y + 3 y^{2} z + 4 z^{2} x$
$\Rightarrow g r a d V = \to ▽ v ($ using vectory identiy $8)$
and $c u r l (g r a d V) = \to ▽ \times \to ▽ V = \to 0$

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