Identidades vectoriales

Mostrar que:
    A × (B × C) + B × (C × A) + C × (A × B) = 0
     ∇ · (f A) = f (∇ · A) + A · (∇ f)
     ∇ × (∇ × A) = ∇(∇ · A) - ∇^2A

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<<Calculus`VectorAnalysis`

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CoordinateSystem

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Cartesian

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Coordinates[]

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{Xx, Yy, Zz}

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SetCoordinates[Cartesian[x, y, z]]

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Cartesian[x, y, z]

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Coordinates[]

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{x, y, z}

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a = {ax[x, y, z], ay[x, y, z], az[x, y, z]} ; b = {bx[x, y, z], by[x, y, z], bz[x, y, z]} ; c = {cx[x, y, z], cy[x, y, z], cz[x, y, z]} ; f = fun[x, y, z] ;

A×(B×C)+B×(C×A)+C×(A×B)=0

∇ ·(f A)=f(∇ ·A)+A·(∇ f)

∇  (∇ A) = ∇ (∇ · A) - ∇^2 A

Created by Mathematica  (August 6, 2004)