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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Vector Algebra

If $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ are $\perp$ then $\overrightarrow a,\:\overrightarrow b\:\overrightarrow c$ are .....

$\begin{array}{1 1} \text{Coplanar} \\(B) \text{Mutually perpendicular} \\ (C) \text{Parallel to one another} \\ (D) \text{Do not lie in one plane}\end{array} $

1 Answer

Given: $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ are $\perp$.
$\Rightarrow\:(\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a).(\overrightarrow a+\overrightarrow b+\overrightarrow c)=0$
$\Rightarrow\:3[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=0$
$\Rightarrow\:\overrightarrow a,\:\overrightarrow b\:\overrightarrow c$ are coplanar.
answered Dec 7, 2013 by rvidyagovindarajan_1
 

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