The points are collinear, and there is an infinite number of planes that contain a given line. A plane containing the line can be rotated about the line by any number of degrees to form an unlimited number of other planes.
If, on the other hand, the points are not collinear, then the plane has no wriggle room: it is stuck fast in one place - there can be only one plane containing all the points. Provided they are non-colinear, three points will define a plane.
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
Only one plane can pass through 3 non-collinear points.
exactly nine planes! * * * * * I would have said 4 - corresponding to the four faces of a tetrahedron. Of course, non-collinear does not mean non-coplanar so all four points could be in the same single plane!
Three collinear points don't define a plane."Define" means narrow it down to one and only one unique plane, so that it can't be confused with any other one.There are many different planes (actually infinite) that can contain three collinear points, so no unique plane is defined.
4
You can have an infinite number of planes passing through three collinear points.
If the points are collinear, the number of possible planes is infinite. If the points are not collinear, the number of possible planes is ' 1 '.
Only one if they are non-collinear. An infinite number if they are collinear.
three
three
Exactly one.
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.
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
In Euclidean geometry, only one.
infinite
There will always be a single plane through all three points.
4 planes.