three
You can have an infinite number of planes passing through three collinear points.
three
Only one if they are non-collinear. An infinite number if they are collinear.
Exactly one.
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
There will always be a single plane through all three points.
infinite
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.
10!
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.
Only one plane can pass through 3 non-collinear points.
Exactly one.