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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Vector Algebra
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Q)

If $\overrightarrow a,\:\overrightarrow b$ are two non zero and non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

$\begin{array}{1 1} \overrightarrow a+\overrightarrow b \\ \overrightarrow a\times\overrightarrow b \\ \overrightarrow a-\overrightarrow b \\ \overrightarrow b\times\overrightarrow a\end{array} $

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A)
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  • $\overrightarrow r.\hat i+\overrightarrow r.\hat j+\overrightarrow r.\hat k=\overrightarrow r$
$[\overrightarrow a\:\overrightarrow b\:\hat i]=(\overrightarrow a\times\overrightarrow b).\hat i$
$[\overrightarrow a\:\overrightarrow b\:\hat j]=(\overrightarrow a\times\overrightarrow b).\hat j$ and similarly $[\overrightarrow a\:\overrightarrow b\:\hat k]=(\overrightarrow a\times\overrightarrow b).\hat k$
$\therefore\:[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=(\overrightarrow a\times\overrightarrow b)$
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