Collinear vectors have the same direction.
A vector is, in the field of physics , a magnitude that is defined through its point of application, its direction, its sense and its magnitude. Depending on their characteristics and the context in which they act, we can differentiate between different classes of vectors, such as coplanar vectors , non-coplanar vectors , opposite vectors , resulting vectors , unit vectors and concurrent vectors , among others.
In the case of collinear vectors , these are those that appear on the same line or that are parallel 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 theory in the area of Geometry, it can be said that two vectors are collinear when they have the same direction since, in that case, they are directors of parallel lines. Of course, they do not necessarily have the same meaning.
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 passes through the pulley in question. When pulling the rope, two forces act: one created by the tension exerted by the rope upwards and another that is directed downwards and is represented by the weight of what you want to move. It can be said, therefore, that two collinear vectors act on the string.
When it comes to graphically representing the aforementioned collinear vectors, it is important to take into account several relevant aspects. Specifically, to do it properly you have to choose to use both direction and meaning, passing through the point of application and the module. The latter must be known that it is given by the length of each vector in question based on a scale that has previously been determined.
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 reflected in their name: non-collinear vectors. Of these we can highlight the following signs of identity:
-They are 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 creation and use of a diagram plays a fundamental role.
-When it comes to adding these non-collinear vectors, it must be taken into consideration that they must be referred to the same physical magnitude.
It is important to mention that a null vector (whose module is equal to 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 points fit on all lines.