**1**]

\begin{equation}

\mathbf{u} + \mathbf{v} = \left( u_1 + v_1 +, \ldots, + u_n + v_n \right)

\end{equation}

One property of vector addition is known as the commutative property [

**2**]:
\[ \mathbf{A} + \mathbf{B} = \mathbf{B} + \mathbf{A} \]

Another property of vector addition is known as the associative property [

**2**]:
\[ \left( \mathbf{A} + \mathbf{B} \right) + \mathbf{C} = \mathbf{B} + \mathbf{A} \]

**References:**

[

**1**] W. Kaplan.

*Advanced Calculus*, 5th ed. Addison-Wesley. 2002

[

**2**] A. I. Borisenko and I. E. Tarapov.

*Vector and Tensor Analysis with Applications,*(translated by R. A. Silverman). Dover Publications Inc., Mineola, NY. 1979 (originally published in 1968 by Prentice-Hall, Inc.

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