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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are three vectors of magnitude $3,4,5$ respectively. If each vector is $\perp$ to sum of the other two vectors then $|\overrightarrow a+\overrightarrow b+\overrightarrow c|=?$

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Given: $|\overrightarrow a|=3,\:|\overrightarrow b|=4,\:|\overrightarrow c|=5$
and $\overrightarrow a.(\overrightarrow b+\overrightarrow c)=\overrightarrow b.(\overrightarrow c+\overrightarrow a)=\overrightarrow c.(\overrightarrow a+\overrightarrow b)=0$
$\Rightarrow\:\overrightarrow a.(\overrightarrow b+\overrightarrow c)+\overrightarrow b.(\overrightarrow c+\overrightarrow a)+\overrightarrow c.(\overrightarrow a+\overrightarrow b)=0$
$\Rightarrow\:2(\overrightarrow a.\overrightarrow b+\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a)=0$
$|\overrightarrow a+\overrightarrow b+\overrightarrow c|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+|\overrightarrow c|^2+2(\overrightarrow a.\overrightarrow b+\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a)$
$\therefore |\overrightarrow a+\overrightarrow b+\overrightarrow c|=\sqrt {50}=5\sqrt 2$
answered Nov 30, 2013 by rvidyagovindarajan_1

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