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If veca, vecb and vecc be three non-copl...

If `veca, vecb and vecc` be three non-coplanar vectors and a',b' and c' constitute the reciprocal system of vectors, then prove that
`i. vecr=(vecr.veca')veca+(vecr.vecb')vecb+(vecr.vecc')vecc`
ii. `vecr= (vecr.veca)veca'+(vecr.vecb)vecb' + (vecr.vecc) vecc'`

A

`vecr = (vecr.veca)veca_(1) +(vecr.vecb)vecb_(1)+(vecr.vecc)vecc_(1)`

B

`vecr =(vecr.veca)veca+(vecr.vecb)vecb+(vecr.vecc)vecc`

C

`vecr=(vecr.veca_(1))veca +(vecr.vecb_(1))vecb + (vecr.veca_(1))vecc`

D

None of these

Text Solution

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The correct Answer is:
A, C
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