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Question
$\overrightarrow a \,,\overrightarrow b \,,\overrightarrow c $ are $3$ vectors, such that

$\overrightarrow a + \overrightarrow b + \overrightarrow c = 0$ , $\left| {\overrightarrow a } \right| = 1\,\,\,\left| {\overrightarrow b } \right| = 2,\,\,\,\left| {\overrightarrow c } \right| = 3,$,

then ${\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a }$ is equal to :
$1$
$0$
$-7$
$7$

Solution

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