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Opposites Vectors

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In the field of physical , the vectors are magnitudes which are defined by their amount, their address, their point of application and their meaning. It is possible to classify vectors 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 equal magnitude although opposite direction because the address It also points out the meaning.

The idea of opposite vectors, in short, it implies working with two vectors that have the same magnitude (that is, the same module) and the same direction although in 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 also its negative .

Take the case of RS vector and the MN vector . The coordinates of the vector RS are (4,8)while the coordinates of the vector MN are (-4, -8). Both vectors are opposite vectors: the vector MN is the negative vector of the vector RS . In a graphic representation, it would be clear how both vectors have the same module (they would occupy the same space in the scheme) 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 zero vector since its module is equal to 0 (lacks extension).

The graphic representation of the vectors always helps us to understand more clearly their characteristics, 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 for a moment the components (or terms) of the vector, which we can define as its values ​​on 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 25-meter vector with a 50 ° angle to the North West is opposite to the 25 meter vector with a 50 ° angle to the South East.

How can we represent this pair of opposite vectors in a graph? First, it should be noted that we are faced with two-dimensional vectors, since we have simply provided respective information to two axes , which are usually identified with the letters X and AND . Therefore, the first step is to draw the two axes.

Next, we must consider for a second the location of each "hemisphere" within the space we have just drawn: we can say that the Northwest is in the upper left quadrant. As a last step of this stage of previous preparation, it is necessary to establish a scale , to know how much the 25 meters in our sheet will be. So, 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 transporter, we must determine the point through which the first vector must pass, which will have its origin in (0,0), that is, at the vertex of the Cartesian axes. Taking into account the aforementioned scale, we draw a line of the relevant measure and, voila. To respect the conventions and that our graph is easy to read by other people, it is recommended to draw two small lines at the top end of the vector as an "arrowhead", as well as indicate the internal angle with a curved line.

Having the main vector, drawing its opposite is much simpler, since it is not necessary to calculate the angle nor its length, but just align a ruler to the first and draw it to the Southeast (the lower right quadrant) with the same extension.

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