The operation with the vectors is graphically presented. By moving the vector endpoints the vectors can be changed. The red vector is the result of the vector addition. The dotted lines are the parallel moved vectors.

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v_{x} =

v_{y} =

w_{x} =

w_{y} =

The addition of vectors is done in Cartesian coordinates componentwise. The vector addition is commutative and associative.

Geometrically, the resulting vector can be constructed by one of the vectors is parallel shifted to the other end point of the vector. The connection from the start point of the first vector to the end point of the second vector is the resultant of vector of vector addition.

$\overrightarrow{v}+\overrightarrow{w}=\left(\begin{array}{c}{v}_{1}\\ {v}_{2}\\ \vdots \\ {v}_{n}\end{array}\right)+\left(\begin{array}{c}{w}_{1}\\ {w}_{2}\\ \vdots \\ {w}_{n}\end{array}\right)=\left(\begin{array}{c}{v}_{1}+{w}_{1}\\ {v}_{2}+{w}_{2}\\ \vdots \\ {v}_{n}+{w}_{n}\end{array}\right)$

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