Vector addition – What it is, definition and concept

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.

Vector p

Vector P
Vector p

We divide the vector p in two vectors:

Coordinates of vector p

Vector r

Vector r

We divide the vector r in two vectors:

Coordinates of vector r

We can join two vectors by joining the back of one vector with the front of another vector, like this:

Vector addition scheme

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:

Vector outline

Commutative property

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.

Sum of vectors p and r


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:

Vectors vyw

First, we divide each vector into its coordinates of the form:

Coordinates of vectors v and w

Second, we add the corresponding coordinates of each vector:

Sum of vectors v and w


Sum of vectors v and w

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