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

If $\overrightarrow p,\overrightarrow q$ are non collinear vectors, then $[\hat i\:\overrightarrow p\:\overrightarrow q]\hat i+[\hat j\:\overrightarrow p\:\overrightarrow q]\hat j+[\hat k\:\overrightarrow p\:\overrightarrow q]\hat k$=?

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  • $\overrightarrow a.\hat i+\overrightarrow a.\hat j+\overrightarrow a.\hat k=\overrightarrow a$
$[\hat i\:\overrightarrow p\:\overrightarrow q]\hat i=[\hat i.(\overrightarrow p\times\overrightarrow q)]\hat i$
$[\hat j\:\overrightarrow p\:\overrightarrow q]\hat j=[\hat j.(\overrightarrow p\times\overrightarrow q)]\hat j$
$[\hat k\:\overrightarrow p\:\overrightarrow q]\hat k=[\hat k.(\overrightarrow p\times\overrightarrow q)]\hat k$
$\therefore\:[\hat i\:\overrightarrow p\:\overrightarrow q]\hat i+[\hat j\:\overrightarrow p\:\overrightarrow q]\hat j+[\hat k\:\overrightarrow p\:\overrightarrow q]\hat k=$
$\overrightarrow p\times\overrightarrow q$
answered Nov 1, 2013 by rvidyagovindarajan_1
 

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