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Definition

If 2 vectors are in the same \(n\)-dimensional space, then they can be added. Addition happens cooridnate-wise. In \(n\)-dimensional space, the formula is the following: \[< a_1, a_2, \dots, a_n > + < b_1, b_2, \dots, b_n > = < a_1 + b_1, a_2 + b_2, \dots, a_n + b_n >\]

For an example in 2-dimensions: \begin{align} <2,3>+<4,6> & = <2+4, 3+6> \\ & = <6, 9> \end{align} There is no definition of a sum of 2 vectors of different dimensions.
\[<3,2> + <1,3,4> = \text{undefined}\]

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Properties of the Vector Addition

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