I know that with a point in 3D you would find ρ,θ,φ - for a plane like z = 9 how would I write ρ?

I'm guessing that θ might be 2π, but I'm lost as to how to find ρ and φ for a plane instead of a point.

Thanks!

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I know that with a point in 3D you would find ρ,θ,φ - for a plane like z = 9 how would I write ρ?

I'm guessing that θ might be 2π, but I'm lost as to how to find ρ and φ for a plane instead of a point.

Thanks!

just substitute in the appropriate expressions in spherical coordinates.

\(\displaystyle x=\rho \sin(\theta)\cos(\phi),~y=\rho \sin(\theta)\sin(\phi),~z=\rho \sin(\theta)\)

for example \(\displaystyle z=9 \Rightarrow \rho \sin(\theta) = 9,~\rho = 9\csc(\theta)\)

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I hope you understand that what you will get is not specific

I know that with a point in 3D you would find ρ,θ,φ - for a plane like z = 9 how would I write ρ?

I'm guessing that θ might be 2π, but I'm lost as to how to find ρ and φ for a plane instead of a point.

Thanks!

You can do something similar for y=3, but then all three coordinates are involved.

But

There is an error in above.

just substitute in the appropriate expressions in spherical coordinates.

\(\displaystyle x=\rho \sin(\theta)\cos(\phi),~y=\rho \sin(\theta)\sin(\phi),~z=\rho \sin(\theta)\)

for example \(\displaystyle z=9 \Rightarrow \rho \sin(\theta) = 9,~\rho = 9\csc(\theta)\)

\(\displaystyle z = \rho \cos(\theta)\) and thus \(\displaystyle z=9 \Rightarrow \rho = 9 \sec(\theta)\)

my apologies