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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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If $\overrightarrow a+2\overrightarrow b+3\overrightarrow c=\overrightarrow 0$, then $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a=?$

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Given: $\overrightarrow a+2\overrightarrow b+3\overrightarrow c=\overrightarrow 0$
$\Rightarrow\:\overrightarrow a=-2\overrightarrow b-3\overrightarrow c$
$\therefore\:\overrightarrow a\times\overrightarrow b+\overrightarrow b+\overrightarrow c+\overrightarrow c\times\overrightarrow a=-3(\overrightarrow c\times\overrightarrow b)+(\overrightarrow b\times\overrightarrow c)-2(\overrightarrow c\times\overrightarrow b)$
$=6(\overrightarrow b\times\overrightarrow c)$
answered Dec 8, 2013 by rvidyagovindarajan_1

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