# Rules for adding vectors

In order to perform the addition operationvectors, there are several ways, which, depending on the situation and type of vectors considered, can be more convenient to use. Let's look at the rules for adding vectors:

## Rule of the triangle

The rule of the triangle is as follows: in order to add two vectors x, y it is necessary to construct a vector x so that its origin coincides with the end of the vector y. Then their sum will be the value of the vector z, and the origin of the vector z will coincide with the beginning of the vector x, and the end with the end of the vector y.

The triangle rule helps, if the number of vectors that need to be summed is no more than two.

## Rule of a polygon

The polygon rule is the simplest and most convenientto add any number of vectors on a plane or in space. The essence of the rule is the following: when adding vectors, you need to sequentially align them one by one so that the beginning of the subsequent vector coincides with the end of the previous one, and the vector that closes the formed curve is the sum of the terms of the vectors. This is illustrated graphically by the equation w = x + y + z, where the vector w is the sum of these vectors. In addition, it should be noted that the sum does not change from the change in the places of the terms of the vectors, that is (x + y) + z = x + (y + z).

## The parallelogram rule

The parallelogram rule is used to addvectors that originate from a single point. In this rule, it is said that the sum of the vectors x and y, having a beginning at one point, will be the third vector z originating also from this point, and the vectors x and y are the sides of the parallelogram, and the vector z is its diagonal. In this case, it also does not matter in which order the vectors will be added.

Thus, the polygon rule, triangle rule, and parallelogram rule help to solve the problem of adding vectors of absolutely any complexity, both on the plane and in space.