XPost: alt.recovery.aa, alt.social-security-disability, uk.rec.psychic
The point(s) resulting from the intersection of a sphere with a line, (if
the line intersects the sphere):
http://www.stonetabernacle.com/sphere-line.html
The point or equation of the circle resulting from the intersection of a
plane with a sphere, (if the plane intersects the sphere):
http://www.stonetabernacle.com/sphere-plane_1.html
An n-dimensional plane is defined by n noncolinear points, and its normal
the cross product of (n-1) lines adjoining them. The case can be extended
to find the n-dimensional circle resulting from the intersection of the n-dimensional sphere and the n-dimensional plane.
In the case of the (n-1) point(s) resulting from the intersection of the n-dimensional line with the n-dimensional sphere, all that is involved in
its calculation is the dot product.
The fact that points in spaces of dimension higher than 3 can't be
visualized has of course nothing to do with their existence.
I posted this earlier but since then edited the pages so they can be read easier.
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