With respect to right-handed coordinates, let v = [y + z; z + x; x + y] and g = xyz, find curl (gv).
asked Apr 10, 2017 in Calculus Answers by chstk8568 (240 points)

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With respect to right-handed coordinates, let v = [y + z; z + x; x + y] and g = xyz, find curl (gv).

F = F1.i + F2.j + F3.k

Curl(F)  = {δF3/δy – δF2/δz}.i – {δF3/δx – δF1/δz}.j + {δF2/δx – δF1/δy}.k

V = [y + z, z + x, x + y],   g = xyz

gV = {xy^2z + xyz^2, xyz^2 + x^2yz, x^2yz + xy^2z]

curl(gV) = [(x^2z + 2xyz) – (2xyz + x^2y), - (2xyz + y^2z) + (xy^2 + 2xyz), (yz^2 + 2xyz) – (2xyz + xz^2)]

curl(gV) = [x^2z – x^2y, -y^2z + xy^2, yz^2 – xz^2]

curl(gV) = [x^2(z – y), y^2(x – z), z^2(y – x)]

answered Apr 15, 2017 by Fermat Level 11 User (78,340 points)

I'm so pleased you answered these vector questions. You've helped a lot of people I'm sure,---including me!

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