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Can three noncollinear points be contained on one plane?
Yes. You require three non-collinear points to uniquely define a 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.
If three distinct points are not col-linear how many planes can possibly contain the three points?
Three non-co-linear points are sufficient to uniquely define a single plane.
Why is a plane not defined by three given points?
it is, unless all three points are in the same line (Your "Why" should have be "When")
Are three collinear points coplanar?
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.
How many non-collinear points are needed to create a plane?
To create a plane, infinitely many. To uniquely determine a plane, just three.
Does a line lie in only one plane?
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.)
Infinite width and length and can be determined by three points?
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.
How many planes can be formed with four non 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.
What is advantage of three legged stool?
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
Do a line and a point outside the line determine a 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.
What would happen if three collinear points are used to define a plane?
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.
