With respect to right-handed coordinates, let v = [y + z; z + x; x + y] and g = xyz, find curl (gv).
in Calculus Answers by Level 1 User (240 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

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)]

by Level 11 User (81.5k points)

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

Related questions

1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,256 questions
90,492 answers
2,140 comments
81,465 users