Coplanar vectors lie in the same plane.
The term vector can be used in different ways. In the field of physics , a vector is a magnitude that is defined by its point of application, its direction, its sense and its magnitude.
Coplanar , for its part, is a concept that is not part of the dictionary of the Royal Spanish Academy ( RAE ). However, the adjective coplanar does appear, which refers to figures or lines that are in the same plane .
Concept of coplanar vectors
Although the notion is incorrect according to the grammatical rules of our language, the idea of coplanar refers to points that are in the same plane (that is, they are coplanar points). When the point does not belong to said plane, it is considered non-coplanar with respect to the others.
Coplanar vectors , therefore, are vectors that are in the same plane . To determine this question, we resort to the operation known as the triple scalar product or mixed product . When the result of the triple scalar product is equal to 0 , the vectors are coplanar (as are the points they join).
Some considerations
In this sense, starting from the meaning and meaning of coplanar vectors, we can determine two notable statements that are worth taking into consideration:
-If you only have two vectors, they will always be coplanar.
-However, if there are more than two vectors, it may happen that one of them is not coplanar.
-Three vectors are coplanar or coplanar if their mixed product is equivalent to zero.
-Three vectors can be said to be coplanar or coplanar if they turn out to be linearly dependent.
Understanding the notion of coplanar vectors can be complex.
Operations with coplanar vectors
These guidelines also allow us to affirm that, when the result of the aforementioned operation is different from 0, the vectors are non-coplanar. This means that these vectors, unlike coplanar vectors, are not part of the same plane.
For example: the vectors A (1, 1, 2) , B (1, 1, 1) and C (2, 2, 1) are coplanar vectors since their triple scalar product is 0 .
Other classes of vectors
In addition to this type of coplanar vectors, it must be taken into account that there are others that are also studied, such as these:
-Concurrent vectors, which are identified because their guidelines or lines of action intersect at a specific point.
-Parallel vectors, which are vectors that are characterized because the lines that contain them are parallel.
-Sliding vectors, which have the peculiarity that, along their guideline, they can proceed to change position.
-Position vectors. They are also known as fixed vectors and are identified because they have a fixed origin and because they record what a force is in space.
-Colllinear vectors, which are identified because their lines of action are on the same line.
-Free vectors. They are those that have the ability to move towards parallel lines or along their directions without being forced to undergo modifications of any kind.