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.
Three points can lie in more than one plane if they are not collinear. If the three points are non-collinear, they define a unique plane, but if they are collinear, they can lie on infinitely many planes that contain that line. Additionally, if you consider different orientations or positions of planes that intersect the line formed by the collinear points, these also contribute to the existence of multiple planes. Therefore, the arrangement and relationship of the points determine how many planes can contain them.
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.