The vector is a concept with several meanings. If we focus on the field of physics, we will find that a vector is a quantity defined by its direction, its direction, its quantity and its point of application.
The adjective coplanar, in turn, 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 of the Royal Spanish Academy (RAE). Instead, this entity mentions the word coplanar. Vectors that are part of the same plane, therefore, are coplanar vectors. Instead, vectors that belong to different planes are called non-coplanar vectors.
It is established, therefore, that non-coplanar vectors, not being in the same plane, it is essential to go to three axes, for a three-dimensional representation, to expose them. To determine whether vectors are coplanar or non-coplanar, it is possible to use 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 not coplanar (equal to the join points). Following the same reasoning, we can say 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). Consider the case of vectors A (1, 2, 1), B (2, 1, 1), and C (2, 2, 1). If we carry out the triple dot product operation, we will see that the result is 1. Being different from 0, we can say that they are 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 refer to the following:
-The module, which is the size of the vector in question. To determine it, it is necessary to start from its end and its point of application.
-The direction, which can be of very different types: up, down, horizontally to the right or to the left… It comes to be determined, of course, from the arrow at one of its ends.
-The application point, already mentioned above, which is the origin from which the vector begins to work.
-The direction, which is the orientation acquired by the line on which the vector in question is located. In this case, we can determine that this direction can be horizontal, oblique or vertical. In many scientific and mathematical areas, these vectors, coplanar and non-coplanar, are used, but also many others that exist. We refer to the concurrent, the collinear, the unitary, the angular, the free…
With any of them, operations such as sums or even products can be carried out, which will be carried out using the different existing methods and procedures.
