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I'm looking for a free, interactive program that allows me to graphically draw vectors, and at the same time display specified dot products, magnitudes, etc. as I move/resize the vectors. It can be either web-based or otherwise, doesn't really matter, but must have the above capabilities.

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You could try GeoGebra. I'm not sure if this does everything you want it to but it definitely can let you draw and resize vectors, as well as do calculations with them.

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    $\begingroup$ geogebra.org $\endgroup$
    – wada
    Commented Sep 24, 2020 at 3:48

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