Vectors Can Be Summed Because They Are Movement

The sum of two vectors can be visualized by taking the beginning of one vector and placing it at the end of another vector.

$\left[\begin{array}{c}1\\ 2\end{array}\right]+\left[\begin{array}{c}3\\ -1\end{array}\right]=\left[\begin{array}{c}4\\ 1\end{array}\right]$

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Connections

Vectors Represent Movement

Link Explanation: The linked note describes vectors as instructions for movement. That is why they can be added to together. By moving along the instructions for the first movement, then moving along the instructions for the second movement, you end up at the same location you would have if you just traveled along their sum.

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Reference

https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab