No. The tiniest piece of a plane contains an infinite number of points. But if you
give us just three points, then we know exactly what plane you're talking about,
and it can't be any other plane.
Exactly one.
Infinitely many planes contain any two given points- it takes three (non-collinear) points to determine a plane.
Only one plane can contain three specific points.
Exactly one.
Three non-co-linear points are sufficient to uniquely define a single plane.
Exactly one.
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
Infinitely many planes contain any two given points- it takes three (non-collinear) points to determine a plane.
One.
Only one plane can contain three specific points.
There will always be a single plane through all three points.
Exactly one.
Yes, and in fact it is very likely that two planes will contain exactly one identical line. There are three possibilities:The planes are parallel, but not identical, in which case they contain no identical lines.The planes are not parallel, in which case they contain exactly one identical line.The planes are identical, and contain an infinite number of coplanar lines.
Three non-co-linear points are sufficient to uniquely define a single plane.
3 non-collinear points define one plane.
If the points are collinear, that means there's only one straight line. An infinite number of different planes can be drawn that contain one straight line.
Through any three non-collinear points, exactly one plane can be defined. If the three points are collinear (lying on a single straight line), then an infinite number of planes can be created, as any plane containing that line will also pass through those points. Thus, the relationship between the points determines the number of planes possible.