In the field of physics, vectors are quantities defined by their quantity, their direction, their point of application and their meaning. Vectors can be classified in different ways depending on their characteristics and the context in which they operate.
Opposite vectors are known as those that have the same direction and magnitude, but have opposite directions. By other definitions, opposite vectors have the same magnitude but opposite direction because direction also indicates direction. The idea of opposite vectors, in short, implies working with two vectors that have the same magnitude (that is, the same magnitude) and the same direction, although in opposite directions. 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 also its negative.
Take the case of vector RS and vector MN. The coordinates of the RS vector are (4,8), while the coordinates of the MN vector are (-4, -8). Both vectors are opposite vectors: the MN vector is the negative vector of the RS vector. In a graphical representation, it would be clear how the two vectors have the same magnitude (they would occupy the same space in the diagram), but in opposite directions. It is important to point out that if we add two opposite vectors, we will obtain as a result a null vector, also known as a zero vector since its magnitude is equal to 0 (it has no extension). The graphic representation of vectors always helps us to understand their characteristics more clearly, and in the case of opposites it is also true, thanks in part to the inclusion of another concept: the cardinal points. If we leave aside for a moment the components (or terms) of the vector, which we can define as its values on each Cartesian axis, and simply focus on its magnitude and the angle it makes with the X-axis, then we can say that the vector 25 meters at an angle of 50° north of west is opposite to 25 meters at an angle of 50° south of east. How can we represent this pair of opposing vectors on a graph? First, keep in mind that we’re dealing with two-dimensional vectors, since we’ve just provided information for two respective axes, which are usually identified by the letters X and Y. So the first step is to draw the two axes.
Next, we’ll need to consider for a second the location of each “hemisphere” within the space we’ve just drawn: we can say that Northwest is in the upper left quadrant. As the last step of this preliminary preparation step, it is necessary to establish a scale, to know how the 25 equal meters will be on our sheet. So it remains to draw the two vectors. To do this, we must remember that the angle is formed in relation to the X axis, 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 mentioned scale, we draw a line of the measure in question and, that’s it. To respect conventions and make our chart easier to read for others, it is recommended to draw two small lines at the top of the vector as an “arrowhead”, as well as to indicate the interior angle with a curved line. Having the main vector, drawing its opposite is much easier since it is not necessary to recalculate the angle or its length, but simply align a ruler with the first one and draw it in a Southeast direction (lower right quadrant) with the same extension.
