[color=#0000ff]The question [/color]often arises as [b]to the importance of the order i[/b]n which the vectors are added. [br]For instance, if five vectors are added - let's call them vectors [size=150] [math]\vec{a},\vec{u},\vec{v},\vec{b},\vec{w}[/math][/size][size=150][color=#9900ff]-[/color][/size] then will a different resultant be obtained if a different order of addition is used. [br][br][br]Will [math]\vec{a}+\vec{u}+\vec{v}+\vec{b}+\vec{w}[/math] yield the same result as [math]\vec{b}+\vec{a}+\vec{v}+\vec{u}+\vec{w}[/math]? [br][size=150][color=#9900ff]The animation below provides the answer. [/color][/size]

As shown in the animation above, the order in which [b][color=#980000]two or more vectors are added does not effect the outcome. [/color][/b][br][br][br][size=150]Adding [math]\vec{a}+\vec{u}+\vec{v}+\vec{b}+\vec{w}[/math] yields the same result as [math]\vec{b}+\vec{a}+\vec{v}+\vec{u}+\vec{w}[/math].[/size][br][br][list][*] The resultant vector, shown as the red vector, has the same magnitude and direction regardless of the order in which the five individual vectors are added.[br][/*][/list]