Parametric Equation for Plane-Sphere Intersection: How To Guide

[dagar]

I'm trying to find the parametric equation for the curve created by a plane intersecting a sphere. Typical sphere x^2+y^2+z^2=1, and plane x+y+z=0. I need the intersection in parametric form so I can use it as the curve in a line integral. I just need to know how to do this, not someone to do it for me.

Thanks

 

[neurocomp2003]

hehe your in waterloo and you can't do this quesiton? hehe j/k Hows waterloo?

3D surface(sphere) requires to two parametrizations, then substitute into the plane equation and your resulting equation shohuld be rather familiar...
or if you'd like use the plane eq'n form N.P+D=0;

 

[dagar]

This is what I was trying but I couldn't get one of the parameters to disappear. I'm probably missing something obvious, which is quite often the case.

Even Waterloo has students that skip too many classes...

 

[matt grime]

It is the curve x^2+y^2+xy=1/2, how you choose to use that would depend on the integral.

 

[dagar]

Sorry I should have clarified, finding the intersection is pretty trivial, I just never know how to parameterize the thing so I can use it as the curve in a line integral.

 

[neurocomp2003]

parametrization of a sphere is
x=s; y=t; z= ? ...substitue into the plane...get circle equation and arrange to something like (s-A)^2+(t-B)^2= R^2 (this should only been dependent on s,t...and other varaible should have a constant associate with R, or plane variables)
set s=new parametrization...u
and solve t interms of u.

...now you have x(s(u)), y(t(u)),z(s(u),t(u))..