Coplanar
In mathematics, the term coplanar refers to a set of points or vectors that lie within the same plane
In mathematics, the term coplanar refers to a set of points or vectors that lie within the same plane. A plane is a two-dimensional flat surface that extends indefinitely in all directions.
Therefore, when we say that a set of points or vectors is coplanar, it means that all those points or vectors can be contained within a single plane, without any of them going above or below that plane. In other words, they all share the same spatial arrangement and can be represented on the same flat surface.
For example, consider three points A, B, and C in space. If all three points lie on the same plane, we can say that they are coplanar. However, if one of the points is slightly above or below the other two, they would not be coplanar.
It is also important to note that any two points are always considered coplanar, as they lie on a unique line which can be considered as a one-dimensional plane. Similarly, three non-collinear points are always coplanar since they define a unique two-dimensional plane. On the other hand, four or more points can be coplanar or not depending on their spatial arrangement.
Coplanarity is a fundamental concept in geometry and is used in various areas of mathematics, such as vector algebra, linear algebra, and analytic geometry, to analyze the relationships and properties of objects in space.
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