Mechanics

Sum of vectors

Traffic sign representing two-way traffic through the use of two vectors

As we already know, a vector is a mathematical entity that represents a set of oriented line segments, whose function is to provide module, direction and direction information. Let’s consider any two non-zero vectors  and  (figure below).

From the end  , we draw a vector equal to  . Connecting the origin of the first vector with the end of the second vector, we obtain the vector , which is called the sum vector or vector resulting from a and b : .

We can also proceed as indicated in the figure below, that is, from the end of   we draw a vector equal to  . The result we will get is the same as the previous one:

It is important to note that in this case the length of   is not equal to the sum of the lengths of   and  :

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