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If vecrxxvecb=veccxxvecb and vecr|veca t...

If `vecrxxvecb=veccxxvecb` and `vecr_|_veca` then `vecr` is equal to

A

`(vecaxx(veccxxvecb))/(veca.vecb)`

B

`(vecbxx(vecaxxvecc))/(veca.vecb)`

C

`(veccxx(vecaxxvecb))/(veca.vecb)`

D

`(veccxx(vecaxxvecb))/(vecb.vecc)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`vecrxxvecb=veccxxvecb`
`implies(vecr-vecc)xxvecb=vec0impliesvecr-vecc=lamdavecbimpliesvecr=vecc+lamdavecb`
Now,
`vecr_|_vecaimpliesvecr.veca=0implies(vecc+lamdavecb).veca=0implieslamda=-(vecc.veca)/(vecb.veca)`
`:.vecr=vecc-(vecc.veca)/(vecb.veca)vecb=((veca.vecb)vecc-(veca.vecc)vecb)/(veca.vecb)=(vecaxx(veccxxvecb))/(veca.vecb)`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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  2. If the vectots phati+hatj+hatk, hati+qhatj+hatk and hati+hatj+rhatk(p!...

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  3. If vecrxxvecb=veccxxvecb and vecr|veca then vecr is equal to

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  4. If veca, vecb, vecc are any three vectors such that (veca+vecb).vecc=(...

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  5. Let veca=2hati+3hatj-hatk and vecb=hati-2hatj+3hatk. Then , the value ...

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  6. Let veca, vecb, vecc be three unit vectors such that veca. vecb=veca.v...

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  7. If veca, vecb, vecc are three non coplanar, non zero vectors then (vec...

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  8. If the acute angle that the vector alphahati+betahatj+gammahatk makes ...

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  9. If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are ...

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  10. If veca vecb are non zero and non collinear vectors, then [(veca, vecb...

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  11. If vecr is a unit vector such that vecr=x(vecbxxvecc)+y(veccxxveca)+...

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  12. Let veca, vecb, vecc be three vectors such that [(veca, vecb, vecc)]=2...

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  13. If vecb is a unit vector, then (veca. vecb)vecb+vecbxx(vecaxxvecb) is ...

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  14. If veca, vecb, vecc are any three non coplanar vectors, then [(veca+ve...

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  15. If veca, vecb, vecc are any three non coplanar vectors, then (veca+v...

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  16. Let veca, vecb and vecc be three having magnitude 1,1 and 2 respective...

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  17. If veca=hati+hatj+hatk, veca.vecb=1 and vecaxxvecb=hatj-hatk then vecb

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  18. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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  19. If the vectors veca, vecb, vecc and vecd are coplanar vectors, then (...

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  20. (vecaxxvecb).(veccxxvecd) is not equal to

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