Infinitely many planes.
Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.
false
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
one
There are an infinite number of planes that pass through a pair of points. Select any plane that passes through both the points and then rotate it along the line joining the two points.
I would say that there are an infinite number of planes that can pass through a pair of skew lines. In order to find the equation of a plane, all you need is three points. take two points off of one line and one point off of the other line and you should be able to derive the equation of a plane. Since the number of points on a line is infinite, an infinite number of planes can be derived.
There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.
Yes since 3 non-collinear points determine a plane. Of course one can take any two of the three points and draw a line between them. There are an infinite number of planes going through this line. Now pick on more point, not on the line, and those three points uniquely determine a plane.
No, the two planes intersect at a line, which is an infinite number of points.
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.
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.