Vector addition is the operation of adding two or more vectors together, giving another vector as a result. This operation can be carried out both graphically and analytically. Next we will see the two ways of performing this operation.

**Parallelogram law**

The parallelogram law gives the rule for vector addition. Consider two vectors **a** and **b**. The **vector sum **is obtained by placing them head to tail and drawing a parallelogram with the aid of two lines parallel to each vector. The vector sum is a vector that goes from the free tail to the free head:

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On the other hand, the subtraction of the same vectors **a** and **b** can be performed by adding **a** plus the opposite of **b**, that is **-b**:

In the figure bellow both operations are represented:

In the following animation you can move vectors **a** and **b** to see both its addition and its subtraction:

**Vector addition (analytically)**

Suppose now that we have expressed both vectors **a** and **b** using the unit vector notation:

The vector sum **c** is obtained by adding the respective components of both vectors:

In the figure below the three vectors have been represented (in two dimensions for the sake of simplicity) as well as their components:

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