yes
Collinear points
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.
Yes.
Three non-collinear points always define exactly one and only one plane. That's why a 3-legged table or chair never wobbles.
For instance a plane.
Collinear points
There are an infinite number of any kind of points in any plane. But once you have three ( 3 ) non-collinear points, you know exactly which plane they're in, because there's no other plane that contains the same three non-collinear points.
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
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.
When you have three collinear points there is one gradient. I'm not sure what your question is specifically but when points are collinear they have the same gradient.
Yes.
3 non-collinear points define one plane.
Three non-collinear points always define exactly one and only one plane. That's why a 3-legged table or chair never wobbles.
Three
For instance a plane.
False. Three collinear points determine a line while three non-collinear points determine a plane ( A Triangle)
Yes. You require three non-collinear points to uniquely define a plane!