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I want to find the equation of plane passing through a diameter of a sphere, For simplicity let us assume that origin,$(0,0,1)$ and $(0,0,-1)$ are on a diameter, then the points lie on the plane $ax+by+cz=d$ using these points i get $d=0$ and $c=0$, what to do next?

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1 Answer 1

The points $(0,0,1)$, $(0,0,0)$ and $(0,0,-1)$ do not define a plane uniquely. A plane of the form $\{(x,y,z)\in\mathbb{R}^3|ax+by=0\}$ will work for any $a,b\in\mathbb{R}$ not both zero.

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can you define points on a diameter that determine a unique plane? –  Mathematician May 8 '13 at 9:40
    
If you include the origin, you need any two points that are not diametrically opposed. –  Abel May 8 '13 at 9:47
    
so if i have origin and one more point say north pole, can i find one more point not dimaetrically opposed? –  Mathematician May 8 '13 at 9:58
    
Any point on the sphere but the south pole would do. –  Abel May 8 '13 at 10:08

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