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If the vectots phati+hatj+hatk, hati+qha...

If the vectots `phati+hatj+hatk, hati+qhatj+hatk` and `hati+hatj+rhatk(p!=q!=r!=1)` are coplanar, then the value of `pqr-(p+q+r)`, is

A

`0`

B

`-1`

C

`-2`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
If given vectors are coplanar, then
`|(p,1,1),(1,q,1),(1,1,r)|=0impliespqr-(p+q+r)=-2`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. Let veca=2hati+hatj-2hatk and vecb=hati+hatj. If vecc is a vector such...

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  2. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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