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**sum**y

**subtraction**two vector

**y**

*A***, results in another**

*B***vector**, that is to say,

** A** +

**=**

*B***y**

*C***–**

*A***=**

*B*

*C*For the addition and subtraction of vectors different methods are applied depending on whether they have the same direction or not. The main methods are: the direct method, the triangle method and the parallelogram.

**Vector sum**

To add two vectors ** A** y

**adds**

*B***with vector**

*A***That is, the components of each vector are added:**

*B*** A** +

**= (A**

*B*_{x }+ B

_{x}, TO

_{y }+ B

_{y}, TO

_{z }+ B

_{z})

**Example: **Sean ** A **= (3, 2, -4) and

**= (-3, 2, 7), calculate the vector**

*B***+**

*A***.**

*B*** A** +

**= ( 3 + (-3), 2 + 2, -4 – 7) = (0, 4, 3)**

*B***Sum of two vectors with the same direction and the same direction**

- We draw the vector
below the vector*B*, so that they are consecutive, respecting their modules, directions and directions.*A* - The vector adds
+*A*it has as a module the sum of the modules of both, the same direction and the same direction of the given vectors.*B*

The resulting vector ** A** +

**has the sum of**

*B***and of**

*A***, the same direction and the same sense as**

*B***y**

*A***.**

*B***Sum of two vectors with the same direction and the opposite direction**

- We draw the vector
below the vector*B*, so that it is consecutive, respecting its modules, directions and directions.*A* - The vector sum has as a module the difference of the modules of both, the same direction and the direction of the larger vector.

The resulting vector ** A** +

**has as a module the difference of**

*B***and of**

*A***, the same direction and the same sense as**

*B***y**

*A***.**

*B*** Sum of two vectors with different directions**

To add two vectors ** A** y

**forming an angle to each other, two methods are used: the triangle method and the parallelogram method.**

*B***Triangle method**

- We draw the vectors consecutively, that is, the origin of
has to match the end*B*.*A* - The vector adds
+*A*has as its origin the origin of*B*and as an extreme, that of*A*.*B*

**Parallelogram law or method **

- We draw the vector
at the origin of a Cartesian plane respecting its module, direction and direction.*A* - We draw at the origin of
, the vector*A***B**respecting its module, direction and sense. - Lines are drawn parallel to each vector forming a parallelogram.
- The resulting vector will be the diagonal of the parallelogram starting at the origin of the Cartesian plane.

**Vector subtraction**

To subtract two vectors ** A** y

**adds**

*B***with the opposite of vector**

*A***, that is to say:**

*B*** A** -

**=**

*B***+ (-**

*A***)**

*B*The components of the vector ** A** -

**are obtained by subtracting its components.**

*B*** A** -

**= (A**

*B*_{x }- B

_{x}, TO

_{y }- B

_{y}, TO

_{z }- B

_{z})

**Example: **Be ** A **= (5, 2, 4) and

**= (-3, 5, 9), calculate the vector**

*B***-**

*A***.**

*B*** A** -

**= ( 5-(-3), 2-5, 4-9) = (8,-3,-5)**

*B***Opposite vector method**

To subtract two vectors ** A** y

**:**

*B*- Like vector
is the subtraction we must draw its opposite vector; therefore we draw a vector equal to*B*but in the opposite direction.*B* - We apply the parallelogram law.

**Triangle method**

- We draw at the origin of
, the vector*A*respecting its module, direction and sense.*B* - The resulting vector
-*A*will originate from the end of*B*(vector subtracting) and as extreme, the extreme of*B**A*(minuend vector).