Non-coplanar vectors are those that do not lie in the same plane.
Vector is a concept with several meanings. If we focus on the field of physics , we find that a vector is a magnitude defined by its sense, its direction, its magnitude and its point of application.
The adjective coplanar , for its part, is used to describe lines or figures that are in the same plane . It is important to mention, however, that the term is not correct from a grammatical point of view and, therefore, does not appear in the dictionary prepared by the Royal Spanish Academy ( RAE ). This entity mentions, however, the word coplanar .
What are non-coplanar vectors?
Vectors that are part of the same plane, in this way, are coplanar vectors . On the other hand, vectors that belong to different planes are called non-coplanar vectors .
It is established, therefore, that to expose non-coplanar vectors, since they are not in the same plane, it is essential to use three axes, a three-dimensional representation.
To know if the vectors are coplanar or non-coplanar, it is possible to resort to the operation known as the mixed product or triple scalar product . If the result of the mixed product is different from 0 , the vectors are non-coplanar (the same as the points they join).
Continuing with the same reasoning, we can affirm that when the result of the triple scalar product is equal to 0 , the vectors in question are coplanar (they are in the same plane).
Take the case of vectors A (1, 2, 1) , B (2, 1, 1) and C (2, 2, 1) . If we perform the triple scalar product operation, we will see that the result is 1 . Since it is different from 0 , we are able to maintain that these are non-coplanar vectors .
To find out if certain vectors are coplanar or non-coplanar, the operation known as triple scalar product can be performed.
Some features
It is also important to know, when working and studying vectors, whether non-coplanar or any other type, that they have four fundamental characteristics or hallmarks. We are referring to the following:
-The module, which is the size of the vector in question. To determine it you have to start from what its end is and the point of application.
-The direction, which can be of very different types: up, down, horizontally to the right or left... It is determined, logically, based on the arrow at one of its ends.
-The point of application, already mentioned above, which is the origin from which the vector proceeds to operate.
-The direction, which is the orientation acquired by the line in which the vector in question is located. In this case, we can determine that this direction can be horizontal, oblique or vertical.
In numerous scientific and mathematical areas, the use of these vectors, coplanar and non-coplanar, but also many others that exist, is used. We are referring to the concurrent, the collinear, the unitary, the angular, the free...
With any of these, operations such as sums or even products can be carried out, which will be undertaken using the different existing methods and procedures.