Mechanics

Spatial orientation

The lines r, set have the direction in common. The line segments PQ, RS and MN have the same direction

When we study Physics, we come across different concepts, formulas, experiments, etc. We use measurement units, for example, to characterize well the physical quantities we study.

When we say that a body has a mass of 200, it is necessary to characterize this mass in kilograms or grams. Therefore, when we say that it has a mass of 200 g we have a better idea of ​​the mass of the body. These physical quantities are called scalar quantities.

In other situations, there is a need for a better identification of the physical quantity. This is the case of physical quantities known as vector quantities. In these cases, the physical quantity needs an intensity (number followed by a unit of measurement) and its spatial orientation (direction and direction).

Spatial orientation (direction and direction)

We say that two lines have the same direction when they are parallel . Two or more line segments have the same direction when they are on the same line or when they are on parallel lines, that is, the direction of a line segment is the same as the direction of the line supporting that segment (figure). When this is not the case, the lines will have different directions.

Let’s consider a line segment AB . On this segment we can imagine two directions of travel: one from A to B, the other from B to A. Then we can consider two segments with different orientations: the oriented segment  and the oriented segment .

The oriented segments MN and PQ, represented in the figure below, have the same direction (ie, the direction of the line r) and opposite directions; while CD and RS have the same direction and the same sense.

Notice that we naturally and intuitively adopt the following notations and nomenclature: given an oriented segment AB, A is the origin and B is the endpoint. See the figure below:

An oriented segment  , where A coincides with B, is called a null segment . In reality, the null segment corresponds to a point and, as such, admits of any direction and sense.

In the figure below, the oriented segment   has a length of AB, which is called a module and can be placed in any unit. The segment   has unit length u . The oriented segment  has length 2u, so the modulus of the oriented segment is   e  . Likewise, we have: 

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