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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.

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โˆ™ 2009-09-08 14:23:33
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Q: What would happen if three collinear points are used to define a plane?
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Related questions

How many non-collinear points define a plane?


Can three noncollinear points be contained on one plane?

Yes. You require three non-collinear points to uniquely define a plane!

Can 3 collinear points define a plane?

No, they have to be noncolinear, that is they all can't be on the same line.

If four points are collinear they are also coplaner?

I dont think that "If four points are collinear they are also coplaner," is the same thing as "If four points are coplaner they are also collinear,". The definition of collinear is at least three points on the same line. To define a plane is to have threenoncollinear points.

How many different lines are determined by 3 non collinear points?

Any three non-collinear points will define a single plane. A plane is composed of an infinite number of distinct lines.

Can noncollinear parts lie on the same plane?

Yes. In fact any three points that are not collinear define a plane and therefore MUST lie on a plane.

How many of non collinear points in plane?

Infinitely many. There are infinitely many points in the plane and although any pair of points define a line, no matter how many lines you are given, it is always possible to find a point that is not on any of them - that is, a point that is not collinear.

Are points that are collinear also coplanar explain?

Points that are collinear will be located on the same line. A line is a subset of a plane. Therefore, Yes, points that are collinear will be located on the same plane.

Do 3 non collinear points lie in at least 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.

How many non collinear points are needed to create a plane?

To create a plane, infinitely many. But to uniquely define one, 3 are enough.

How many different planes are determined by three noncollinear points?

3 non-collinear points define one plane.

How can you name a line and 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.

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