Mechanics

Vector concept

Geometric representation of a vector, with origin in A and end in B

When working with vector quantities, we use vector algebra , which operates with a mathematical entity called vector . For what interests us, we can conceptualize vector as the mathematical entity that represents the set of oriented line segments that have the same module, the same direction and the same direction.

vector representation

The vector is represented  by an oriented line segment with origin at A and end at B. The length of this segment represents the magnitude of the vector on a graphic representation scale. If the vector   is representing a vector quantity, we can use the notation  (in which the letter representing the quantity is used with an arrow on top, the arrow being always horizontal and to the right). See the figure above.

The general characteristics that define a vector are :

  – intensity

  – direction

  – sense

The definition of the intensity or modulus of a vector is the measure we obtain when we compare a vector with another of the same species, considered as a unit. For example: the magnitude of the speed of a car at a certain instant is 50 km/h, if the velocity vector adopted as unitary is contained 50 times in the considered vector.

The direction of a vector is where its endpoint points.

Some particular vectors

We say that two or more vectors are equal or equivalent if their magnitudes are also equal, if their directions are equal and if they have the same sense. See below the representation of equal vectors:

However, when at least one of the characteristics mentioned above is different, we say that the vectors are different. We call the opposite vector of a vector B the vector -B, which has the same magnitude, the same direction, but its direction is opposite to that of B.

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