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Is it possible that 3 vectors, $\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} =0$ but $|\overrightarrow{a}|$, $|\overrightarrow{b}|$ and $|\overrightarrow{c}|$ do not represent the sides of a triangle, If yes why? and if no why?. I'm trying to get the solution since last 2 days, so kindly help me out...

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For vectors $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$ means exactly that they form a triangle: start to concatenate the vectors at the ending/starting points.

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    ...although if the vectors are parallel, then the triangle is degenerate.2012-10-06
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    well, yes, maybe that's not considered as "representing the sides of a triangle"2012-10-06
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    Depends on who you ask, I guess! :-)2012-10-06
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    can't it be 2 vectors parellel in same direction and 3rd vector having magnitude equal to sum of those 2 and is anti-parellel..?2012-10-07
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    No. If 2 vectors, say $a$ and $b$ are parallel, then $c=-a-b$ is also parallel to them.2012-10-08