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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
+1 vote

The value of $[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\overrightarrow a]$ where $|\overrightarrow a|=1,\:\:|\overrightarrow b|=5\:\:|\overrightarrow c|=3$ is ?

$\begin{array}{1 1} 0 \\ 1 \\ 3 \\ 6 \end{array} $

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1 Answer

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$[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\overrightarrow a]=(\overrightarrow a-\overrightarrow b).\big($$(\overrightarrow b-\overrightarrow c)\times(\overrightarrow c-\overrightarrow a)\big)$
$=(\overrightarrow a-\overrightarrow b).(\overrightarrow b\times\overrightarrow c-\overrightarrow b\times\overrightarrow a+\overrightarrow c\times\overrightarrow a)$
$=(\overrightarrow a-\overrightarrow b).(\overrightarrow b\times\overrightarrow c+\overrightarrow a\times\overrightarrow b+\overrightarrow c\times\overrightarrow a)$
$=\overrightarrow a.(\overrightarrow b\times \overrightarrow c)-\overrightarrow b.(\overrightarrow c\times\overrightarrow a)$
$=[\overrightarrow a\:\:\overrightarrow b\:\:\overrightarrow c]-[\overrightarrow a\:\:\overrightarrow b\:\:\overrightarrow c]=0$
answered Nov 18, 2013 by rvidyagovindarajan_1

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