Paper 3, Section II, C

Vector Calculus | Part IA, 2013

State a necessary and sufficient condition for a vector field F\mathbf{F} on R3\mathbb{R}^{3} to be conservative.

Check that the field

F=(2xcosy2z3,3+2yezx2siny,y2ez6xz2)\mathbf{F}=\left(2 x \cos y-2 z^{3}, 3+2 y e^{z}-x^{2} \sin y, y^{2} e^{z}-6 x z^{2}\right)

is conservative and find a scalar potential for F\mathbf{F}.

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