Colinear points mean that if you draw a (really long) line between any two of them, the line will pass through the others. Or simply: there can exist a straight line that can pass through all of them. These are colinear points: . .... .. One line can pass through all of them: These ar not colinear points: :. If I try to connect any two of them with a line, the third point will not lie on that line.
Yes.
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 '.
In Euclidean geometry, only one.
Infinitely many if the 3 distinct points are collinear. Otherwise just 1.
You can have an infinite number of planes passing through three collinear points.
Colinear points mean that if you draw a (really long) line between any two of them, the line will pass through the others. Or simply: there can exist a straight line that can pass through all of them. These are colinear points: . .... .. One line can pass through all of them: These ar not colinear points: :. If I try to connect any two of them with a line, the third point will not lie on that line.
three
three
Yes.
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, the number of possible planes is infinite. If the points are not collinear, the number of possible planes is ' 1 '.
In Euclidean geometry, only one.
Only one plane can pass through 3 non-collinear points.
Infinitely many if the 3 distinct points are collinear. Otherwise just 1.
There is exactly one line that can pass through two distinct points. This line is uniquely determined by the two points.
No, a circle can never pass through three points of a straight line. The circle will touch 1) no points of the line, 2) one point of the line (which is now tangent to the circle), or 3) two points of the line. A line can contain (at most) twopoints that lie on the line.