Plane Intersecting a Sphere

[Aristarchan]

I was thinking this morning of X,Y and Z axes, visualizing a plane intersecting a sphere at varying depths from it's surface. Would the movement of that plane in a direction perpendicular to it's two dimensions, so that a circle indicating where the sphere intersects with the plane changes diameter but stays centered on the same point in that plane, be always referred to as movement along a Z axis?

 

[lev888]

Not sure I understand the question. How exactly is the coordinate system defined? In any case, a plane moving in the direction of its normal will intersect any sphere in the way you describe.

 

[pka]

I was thinking this morning of X,Y and Z axes, visualizing a plane intersecting a sphere at varying depths from it's surface. Would the movement of that plane in a direction perpendicular to it's two dimensions, so that a circle indicating where the sphere intersects with the plane changes diameter but stays centered on the same point in that plane, be always referred to as movement along a Z axis?

Consider the sphere \(x^2+y^2+z^2=25\) see here.
Now the points \(P_1: (5,0,0),~P_2,~(0,5,0)~\&~P_3,~(0,0,5)\) are on that sphere.
Thus the plane determined by those points is \(x+y+z=5\) SEE HERE
Now we have a model for your question. Please re-frame your question.

 

[LCKurtz]

I had a little time to kill, so here's an animation showing a plane passing through a sphere, intersecting in various size of circles:

Not sure what the OP's question is, but the plane can cut the sphere at any angle.