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If $|\overrightarrow a|=5, \:|\overrightarrow b|=3\:|\overrightarrow c|=4$ and $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$ then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=?$

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Given: $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$
$\Rightarrow\:\overrightarrow a$ is along $\overrightarrow b\times\overrightarrow c$
$\therefore [\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=\overrightarrow a.(\overrightarrow b\times\overrightarrow c)$
$=|\overrightarrow a||\overrightarrow b\times\overrightarrow c|$
$=|\overrightarrow a|\:|\overrightarrow b|\:|\overrightarrow c|.sin \large\frac{5\pi}{6}$
$60\times \large\frac{1}{2}=$$30$
answered Nov 18, 2013 by rvidyagovindarajan_1

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