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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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    No. If 2 vectors, say $a$ and $b$ are parallel, then $c=-a-b$ is also parallel to them.2012-10-08