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Homework Statement
I wonna calculate the vector area dS of a sphere, but for some reason my result gets mixed areound. I need a trained eye to see where I make a silly mistake.
Homework Equations
Parametrization of a sphere:
(x,y,z) = r(cos[itex]\phi[/itex]sin[itex]\theta[/itex],sin[itex]\phi[/itex]cos[itex]\theta[/itex],cosθ)
The Attempt at a Solution
So ∂r/∂[itex]\phi[/itex] = r(cosθcos[itex]\phi[/itex],-sinθsin[itex]\phi[/itex],sinθ)
and
∂r/∂θ = r(-sin[itex]\phi[/itex]sinθ,cos[itex]\phi[/itex]sinθ,0)
and dS = ∂r/∂[itex]\phi[/itex] x ∂r/∂θ = r2 (sinθcosθcos[itex]\phi[/itex],sin[itex]\phi[/itex]sinθ2, ...) dθd[itex]\phi[/itex]
But the first two terms should be switched around according to my notes! Where do I go wrong? :(