The sum of vectors is to form a chain of vectors where the vector that encompasses all the vectors is the vector of the sum.
In other words, vector sum is the union of vectors by joining the front of one vector with the back of the other and fulfills the commutative property.
A vector of dimension n is a row that contains n real numbers, it is represented through a segment with sense and direction and, it serves to represent physical quantities such as volume, pressure, energy …
The sum of vectors
Dice two vectors p and r, we can perform the following operation. First we will divide the vectors into two vectors to make it easier to operate with them.
We divide the vector p in two vectors:
We divide the vector r in two vectors:
We can join two vectors by joining the back of one vector with the front of another vector, like this:
The result of this union will be the sum of the vector p and vector r, indicated by the black vector p + r. Such that:
The commutative property of vectors appears when we can express the sum of p + r What r + p, that is to say, p + r = r + p. It does not matter the order in which we add the vectors r and p.
The sum of vectors is found in the daily life of mathematics and in all the sciences that depend on them, whether they are statistics, physics, engineering …
Add the following vectors:
First, we divide each vector into its coordinates of the form:
Second, we add the corresponding coordinates of each vector: