# Vector Addition Operation

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A Vector Addition Operation is a vector operation that is an Addition Operation.

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**Counter-Example(s):****See:**Vector Space, Pythagorean Theorem.

## References

### 2014

- http://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction
- Assume now that
**a**and b are not necessarily equal vectors, but that they may have different magnitudes and directions. The sum of**a**and b**is :[math]\displaystyle{ \mathbf{a}+\mathbf{b} =(a_1+b_1)\mathbf{e}_1 +(a_2+b_2)\mathbf{e}_2 +(a_3+b_3)\mathbf{e}_3. }[/math] The addition may be represented graphically by placing the tail of the arrow**b at the head of the arrow**a**, and then drawing an arrow from the tail of a to the head of**b**. The new arrow drawn represents the vector a +**b**, as illustrated below: This addition method is sometimes called the*parallelogram rule*because a and**b**form the sides of a parallelogram and**a**+ b**is one of the diagonals. If**a and**b**are bound vectors that have the same base point, this point will also be the base point of a +**b**. One can check geometrically that a +**b**=**b**+**a**and (a +**b**) +**c**=**a**+ (b**+****c**).

Subtraction of two vectors may also be performed by adding the opposite of the second vector to the first vector, that is,**The difference of**a and**b**is :[math]\displaystyle{ \mathbf{a}-\mathbf{b} =(a_1-b_1)\mathbf{e}_1 +(a_2-b_2)\mathbf{e}_2 +(a_3-b_3)\mathbf{e}_3. }[/math] Subtraction of two vectors can be geometrically defined as follows: to subtract**b**from**a**, place the tails of a and**b**at the same point, and then draw an arrow from the head of b**to the head of**a. This new arrow represents the vector**a**− b, as illustrated below:**a**− b**=**a + (−**b**).

- Assume now that