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- If they do meet each other there are two possibilities. First they can meet in a single point. In this case the plane is tangent to the sphere at the point of intersection. In the other case the sphere and the plane meet in a circle.
www.math.csi.cuny.edu/~ikofman/Polking/sphere.html
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The Intersection Between a Plane and a Sphere. When a spherical surface and a plane intersect, the intersection is a point or a circle. Here, we will be taking a look at the case where it’s a circle. Go here to learn about intersection at a point.
The intersection of the equations $$x + y + z = 94$$ $$x^2 + y^2 + z^2 = 4506$$ is indeed the intersection of a plane and a sphere, whose intersection, in 3-D, is indeed a circle, but if we project the circle onto the x-y plane, we can view the intersection not, per se, as a circle, but rather an ellipse:
May 16, 2017 · I wrote the equation for sphere as $$x^2 + y^2 + (z-3)^2 = 9$$ with center as (0,0,3) which satisfies the plane equation, meaning plane will pass through great circle and their intersection will be a circle. However when I try to solve equation of plane and sphere I get $$x^2 + y^2 + (x+3)^2 = 6(x+3)$$ which does not looks like a circle to me ...
Jan 9, 2015 · How can I find the intersection between the sphere $x^2+y^2+z^2=1$ and the plane $x+y+z=1?$ Context. This is related to a computation of surface integral using Stokes' theorem, Calculate the surface integral $\iint_S (\nabla \times F)\cdot dS$ over a part of a sphere
Dec 30, 2014 · Note: the intersection of a plane and a sphere always forms a circle in the direction of the normal vector to the plane, and an ellipse on the projections on the x, y, z axes.
In the uninteresting case the plane and the sphere miss each other. If they do meet each other there are two possibilities. First they can meet in a single point. In this case the plane is tangent to the sphere at the point of intersection. In the other case the sphere and the plane meet in a circle. It is easy to see that the circle of ...
There are two special cases of the intersection of a sphere and a plane: the empty set of points (O Q > r) and a single point (O Q = r); these of course are not curves. In the former case one usually says that the sphere does not intersect the plane, in the latter one sometimes calls the common point a zero circle (it can be thought a ...
