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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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If $|\overrightarrow a|=2,\:|\overrightarrow b|=3\:and\:|\overrightarrow c|=4$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c=\overrightarrow O$, then $\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a+\overrightarrow a.\overrightarrow b=?$

$\begin{array}{1 1} \large\frac{19}{2} \\ \large\frac{-19}{2} \\ \large\frac{29}{2} \\ \large\frac{-29}{2}\end{array} $

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  • $|\overrightarrow a+\overrightarrow b+\overrightarrow c|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+|\overrightarrow c|^2+2(\overrightarrow a.\overrightarrow b+\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a)$
$|\overrightarrow a+\overrightarrow b+\overrightarrow c|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+|\overrightarrow c|^2+2(\overrightarrow a.\overrightarrow b+\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a)$
$\Rightarrow\:0=4+9+16+2(\overrightarrow a.\overrightarrow b+\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a)$
$\Rightarrow\:\overrightarrow a.\overrightarrow b+\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a=-\large\frac{29}{2}$
answered Oct 30, 2013 by rvidyagovindarajan_1
 

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