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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 non coplanar vectors, then $[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]=?$

$\begin{array}{1 1} (A) 0 \\ (B) -[\overrightarrow a\:\overrightarrow b\:\overrightarrow c] \\ (C) -2[\overrightarrow a\:\overrightarrow b\:\overrightarrow c] \\ (D) -3[\overrightarrow a\:\overrightarrow b\:\overrightarrow c] \end{array} $

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$[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]$$=[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$$\left |\begin{array}{ccc} 1 & 1& 1\\1 &0 &-1\\1&-1& 0\end {array}\right |$
$=-3[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$
answered Nov 21, 2013 by rvidyagovindarajan_1
 

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