Yes, a plane can be uniquely defined by three points as long as the three points are not colinear. (Three points are colinear if there is a straight line that passes through all three points.)
Yes. You require three non-collinear points to uniquely define a plane!
Here is one option: 2 points uniquely define a line so a line can be named after any two points that belong to it. Similarly, three points that are not collinear (all in the same line) uniquely define a plane so a plane can be defined by naming any three non-collinear points in it. There are different - though related - forms in coordinate geometry or in vector algebra.
Three non-co-linear points are sufficient to uniquely define a single plane.
it is, unless all three points are in the same line (Your "Why" should have be "When")
Yes. Three co-linear points define a line, and therefore also lie on a plane, but those three points do not necessarily define only one plane. You need three points, not co-linear, to uniquely define a plane. See Related Links below for more information.
To create a plane, infinitely many. To uniquely determine a plane, just three.
No. A line can lie in many planes. A plane can be defined by three non-linear points. Since a line is defined by only two points, we need another point. (Note that point C alone, or line AB alone belong to an infinite number of planes.)
The shape described is a plane, which is a two-dimensional surface that extends infinitely in both width and length. In geometry, a plane can be uniquely determined by any three non-collinear points on the plane. This is known as the "three-point" or "unique determination" property of a plane. The three points define the plane's orientation and position in three-dimensional space.
Four non-collinear points can form exactly one plane. This is because a plane is defined by three non-collinear points, and adding a fourth point that is not in the same line as the other three does not create a new plane; rather, it remains within the same plane defined by the initial three points. Therefore, all four points lie in the same unique plane.
A plane is defined by at least three non-collinear points. While an infinite number of points can exist within a plane, the minimum requirement to determine a unique plane is three points that do not all lie on the same straight line.
A plane is defined by three points, so a three legged stool is stable because the points on the end of the stool's legs are coplanar
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.