Question

Determine if the vector field F(x, y, z) = (-2xy cos(yz²), x² - z² cos(yz²), 2yz cos (yz²)) is incompressible. Show all work. Can F(x,y,z) = (-2xycos(yz²), x² - z² cos(yz²), 2yz cos(yz²)) be written as the curl of another vector field? Explain.

          Determine if the vector field
F(x, y, z) = (-2xy cos(yz²), x² - z² cos(yz²), 2yz cos (yz²)) is
incompressible. Show all work.
Can F(x,y,z) = (-2xycos(yz²), x² - z² cos(yz²), 2yz cos(yz²)) be
written as the curl of another vector field? Explain.
        
Show more…
Determine if the vector field
F(x, y, z) = (-2xy cos(yz²), x² - z² cos(yz²), 2yz cos (yz²)) is
incompressible. Show all work.
Can F(x,y,z) = (-2xycos(yz²), x² - z² cos(yz²), 2yz cos(yz²)) be
written as the curl of another vector field? Explain.

Added by Pilar J.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Determine if the vector field F(x,y,z) = -2xycos(yz)x - zcos(yz), 2yzcos(yz) is incompressible. Show all work.
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Transcript

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00:01 Show that any vector field of this form is incompressible.
00:04 So we have the, that means a divergence is zero...
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