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Show that the order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors $\vec{A}$ , $\vec{B}$ , and $\vec{C}$ , all having different lengths and directions. Find the sum $\vec{A} + \vec{B} + \vec{C}$ then find their sum when added in a different order and show the result is the same. (There are five other orders in which $\vec{A}$ , $\vec{B}$ , and $\vec{C}$ can be added; choose only one.)
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Final Answer
please see the solution video.
Addition is commutative! (the video explains that formal term at the end)
Solution Video

OpenStax College Physics Solution, Chapter 3, Problem 8 (Problems & Exercises) (3:28)

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