A vector is, in the field of physical, a magnitude which is defined through its point of application, its direction, its meaning and its amount. Depending on their characteristics and the context in which they act, it is possible to differentiate between different classes of vectors, such as coplanar vectors, the non-coplanar vectors, the opposite vectors, the resulting vectors, the unit vectors and the concurrent vectors, among others.

In the case of collinear vectors, these are those that appear in the same line or that result parallels to a certain line. When the relations that maintain their coordinates are equal and the vector product is equivalent to 0, two vectors are collinear.

That is, according to the theory in the area of ​​Geometry, it can be said that two vectors are collinear at the moment that they have the same direction since, in that case, they are directors of parallel lines. Of course, they do not have to have the same meaning necessarily.

Vectors in geometry

Collinear vectors have the same direction.

Example and representation of collinear vectors

We can find examples of collinear vectors in everyday life. Suppose someone tries to lift a heavy object with the help of a pulley. To carry out this action, use a rope that ties the object and that goes through the pulley in question. When pulling the rope, two forces act: one created by the tension that the rope exerts upwards and another that is directed downwards and which is represented by the weight of what is to be moved. It can therefore be said that two collinear vectors act on the string.

When it comes to graphically representing the aforementioned collinear vectors, it is important that several relevant aspects are taken into account. Specifically, to do it properly, you have to choose to use both what is the direction and the sense, going through the point of application and the module. The latter must be known that it is given by what is the length of each vector in question based on a scale that, previously, has been determined.

Arrow

Geometry recognizes different types of vectors according to their characteristics.

The opposite notion

Of course, we must not forget that when we refer to collinear vectors, we inevitably think of others that are their opposites and this is manifested by their name: non-collinear vectors. Of these we can highlight the following identity signs:

-They are the vectors that do not have the same direction.
-In order to obtain the result of these, it is necessary to resort to the use and application of geometric or analytical methods. In the latter, the realization and use of a diagram plays a fundamental role.
-When being able to make the sum of these non-collinear vectors, it must be taken into account that they must be referred to the same physical magnitude.

It is important to mention that a null vector (whose modulus is equal 0) is collinear with respect to all its coplanar vectors (that is, to those vectors that are in the same plane). This is because null vectors are represented as a point, and the points fit on all lines.