Vector It is a concept with several meanings. If we focus on the terrain of the physical , we found that a vector is a magnitude defined by its meaning, its address, its amount and its point of application.
The adjective coplanar , on the other hand, is used to qualify the lines or figures that are in a same plane . It is important to mention, however, that the term is not grammatically correct and, therefore, does not appear in the dictionary that elaborates the Royal Spanish Academy (RAE ). This entity mentions, instead, the word coplanar .
The vectors that are part of the same plane, in this way, are coplanar vectors . On the other hand, vectors belonging to different planes are called non-coplanar vectors .
It is established, therefore, that non-coplanar vectors, as they are not in the same plane, it is essential to go to three axes, to a three-dimensional representation, to expose them.
To know if the vectors are coplanar or non-coplanar, it is possible to appeal to the operation It is known as 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 that unite).
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. Being different from 0, we are in a position to argue that it is about non-coplanar vectors .
It is also important to know, when working and studying vectors, whether they are non-coplanar or of 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, it is necessary to start from what is its end and the point of application.
-The meaning, which can be of very different types: up, down, horizontal to the right or left ... It is determined, of course, 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 becomes the orientation acquired by the line in which the vector in question is located. In this case, we can determine that said direction can be horizontal, oblique or vertical.
In numerous scientific and mathematical areas the use of these vectors, coplanar and non-coplanar, is used, but also of many others that exist. We are referring to the concurrent, the collinear, the unitary, the angular, the free ...
With any of these operations can be carried out such as sums or even products, which will be undertaken by resorting to the different existing methods and procedures.