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.
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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