A problem about surface element

VHAHAHA

I really don't know how to do this question as it asks me to write the surface element of a hemisphere in xyz coordinates. I know how to answer if it is asked in spherical coordinates.

I think this is a tricky question because it asks for the portion da near (0, A, 0) (in xyz) where A is the radius.

I guess da = dydz.

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SammyS

That doesn't look very vector-like.



You say you know the answer in spherical coordinates. What is the answer in spherical coordinates?

VHAHAHA

it should be r^2sin(θ)dθdϕ (unit vector r)

SammyS

What is the value of θ at (x,y,z) = (0,A,0) ? ... the value of r ?

VHAHAHA

it is equal to 90 degree or pi/2
so i should plug this valve to the expression?
i have tried but the question needs me to express it in xyz coor,
how to deal with (unit vector of r)?

SammyS

At the point, (0,A,0), what is [itex]\ \hat{r}\ [/itex] in terms of [itex]\ \hat{i},\,\hat{j},\,\hat{k}\ ?[/itex]

VHAHAHA

O, I get what u mean

at (0 A 0) , the r is along the y axis, so 0i, 1j , 0k ?

SammyS

Just put this with dydz.