In the field of physical, the vector are magnitudes which are defined by their amount, their direction, their point of application and their meaning. Vectors can be classified in different ways according to their characteristics and the context in which they act.
It is known as opposite vectors to those who have the same direction and the same magnitude, but they have opposite senses. According to other definitions, the opposite vectors have the same magnitude but opposite direction because the address it also points out the sense.
Opposite vector examples
The idea of opposite vectors, in short, implies working with two vectors that have the same magnitude (that is, the same module) and the same direction, although with the opposite direction. It can be said that a vector is opposite to another when it has the same magnitude but appears at 180º. In this way, the vector is not only opposite to the other, but it is also its negative.
Take the case of RS vector and the MN vector. The coordinates of the vector RS are (4.8), while the vector coordinates MN are (-4, -8). Both vectors are opposite vectors: the vector MN is the negative vector of the vector RS. In a graphical representation, it would be clear how both vectors have the same module (they would occupy the same space in the diagram) but in the opposite direction.
It is important to note that if we add two opposite vectors we will obtain as result a null vector, also known as a zero vector since its module is equal to 0 (no extension).
The graphic representation of vectors always helps us understand their characteristics more clearly, and in the case of opposites this is also true, partly thanks to the inclusion of another concept: the cardinal points. If we put aside the components (or terms) of the vector, which we can define as its values in each Cartesian axis, and we simply focus on its module and the angle it forms with the axis X, then we can say that the vector of 25 meters with an angle of 50 ° towards the North of the West is opposite to the one of 25 meters with an angle of 50 ° towards the South of the East.
How to represent opposite vectors
How can we represent such a pair of opposite vectors on a graph? In the first place, it should be noted that we are dealing with two-dimensional vectors, since we have simply provided information for two axles, which are usually identified with the letters X and Y. Therefore, the first step is to draw the two axes.
Next, we will have to consider for a second the location of each “hemisphere” within the space that we have just traced: we can say that the Northwest is in the upper left quadrant. As the last step in this preparatory stage, it is necessary to establish a scale, to find out how much the 25 meters will be on our sheet. Then, it only remains to draw the two vectors. To do this, we must remember that the angle is formed with respect to the axis X, that is, the horizontal.
With the help of a protractor, we must determine the point through which the first vector must pass, which will have its origin at (0,0), that is, at the vertex of the Cartesian axes. Taking into account the aforementioned scale, we draw a line of the relevant measurement and, voila. To respect the conventions and that our graph is easy for other people to read, it is recommended to draw two small lines at the top of the vector as an «arrowhead», as well as to indicate the internal angle with a curved line.
Having the principal vector, drawing its opposite is much easier, since it is not necessary to calculate again the angle nor its length, but it is enough to align a ruler to the first and draw it towards the Southeast (the lower right quadrant) with the same extension.