Calcule o rotacional:
F(x, y, z)=(x, x, x z).

Passo 1

O enunciado pede para calcular o rotacional (ou curl) do campo vetorial
F(x,y,z) = (x,;x,;x,z).
Isso envolve usar o operador nablatimes, cujos componentes são
(nablatimesF)1 = partial Rpartial y - partial Qpartial z, (nablatimesF)2 = partial Ppartial z - partial Rpartial x, (nablatimesF)3 = partial Qpartial x - partial Ppartial y,
onde P(x,y,z)=x, Q(x,y,z)=x e R(x,y,z)=x,z.

Passo 2

Calculamos o primeiro componente
(nablatimesF)1 = partial Rpartial y - partial Qpartial z = partial (x,z)partial y - partial (x)partial z = 0 - 0 = 0

Passo 3

Calculamos o segundo componente
(nablatimesF)2 = partial Ppartial z - partial Rpartial x = partial (x)partial z - partial (x,z)partial x = 0 - z = -z

Passo 4

Calculamos o terceiro componente
(nablatimesF)3 = partial Qpartial x - partial Ppartial y = partial (x)partial x - partial (x)partial y = 1 - 0 = 1

Resposta

nablatimesF(x,y,z) = (0,,-z,;1)

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