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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two non zero non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

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  • $(\overrightarrow a.\hat i)\hat i+(\overrightarrow a.\hat j)\hat j+(\overrightarrow a.\hat k)\hat k=\overrightarrow a$
$[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k$
$=((\overrightarrow a\times\overrightarrow b).\hat i)\hat i+((\overrightarrow a\times\overrightarrow b).\hat j)\hat j+((\overrightarrow a\times\overrightarrow b).\hat k)\hat k$
$=\overrightarrow a\times\overrightarrow b$
answered Nov 20, 2013 by rvidyagovindarajan_1
 

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