- #1

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in the form x[t],y[t],z[t]

i know that x^2+y^2+z^2=constant

and that ax+by+cz=0

But i cannot figure out the parametric equation x[t],y[t],z[t] that describes a circle perpendicular to the vector.

- Thread starter okkvlt
- Start date

- #1

- 53

- 0

in the form x[t],y[t],z[t]

i know that x^2+y^2+z^2=constant

and that ax+by+cz=0

But i cannot figure out the parametric equation x[t],y[t],z[t] that describes a circle perpendicular to the vector.

- #2

- 53

- 0

or, phrased in other words, this is the intersection of the plane ax+by+cz=0 and the sphere x^2+y^2+z^2=constant.

in case anybodys wondering, im working on stokes theorem.

in case anybodys wondering, im working on stokes theorem.

Last edited:

- #3

- 9,555

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[tex]\frac {(x-p)^2}{a^2} + \frac {(y-q)^2}{b^2} = 1[/tex]

Then you can parameterize it as:

[tex] x = p + a\cos(t)\ y=q + b\sin(t)[/tex]

and use these to get z on the plane in terms of t also.

- #4

- 9,555

- 766

- #5

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i want to prove that the magnitude of curl is the line integral around a region perpendicular to the curl vector.

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