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lying on the same plane indicates that the normal vector to that plane will always be the same i.e to that point or vector. Another way would be that it should satisfy the standard equation of plane Ax+By+Cz = D in the case of a point or the dot product should equal zero. <A,B,C> . <x-x0, y-y0, z-z0> = 0

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Q: What is lying in the same plane?
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If an object revolves around the sun on the same plane as the planets, it is lying on an ecliptic.


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