What is collinear vectors?
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What Does collinear vectors Mean
A vector is, in the field of physics , a magnitude that is defined through its point of application, its direction, its sense and its quantity. According to their characteristics and the context in which they operate, you can differentiate between different types of vectors, such as coplanar vectors , the non - coplanar vectors , the opposing vectors , the resulting vectors , the unit vectors and the 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 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.
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 being able to graphically represent 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.
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 signs of identity:
-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 consideration that they must be referred to the same physical magnitude.
It is important to mention that a null vector (whose modulus 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 the points fit on all lines.