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If veca,vecb,vecc are three non-coplanar...

If `veca,vecb,vecc` are three non-coplanar vectors and `vecp,vecq,vecr` are their reciprocal then `(lveca+mvecb+nvecc).(veclp+vecmq+vecnr)` is equal to

A

`l^(2)+m^(2)+n^(2)`

B

`lm+mn+nl`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`veca.vecp=vecb.vecq=vecc.vecr=1`
and `veca.vecq=vecb.vecr=veca.vecr=vecb.vecp=vecc.vecp=vecc.vecq=0`
`:.(lveca+mvecb+nvecc).(lvecp+mvecq+nvecr)=l^(2)+m^(2)+n^(2)`
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. If veca, vecb, vecc are three non coplanar, non zero vectors then (vec...

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

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  3. If veca,vecb,vecc are three non-coplanar vectors and vecp,vecq,vecr ar...

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

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

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  6. Let a,b,c be three vectors such that [a b c]=2, if r=l(bxxc)+m(cxxa)+n...

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

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

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

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

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  11. If veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -ha...

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

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

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

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  15. Let veca = 2hati + hatj + hatk, and vecb = hati+ hatj if c is a vecto...

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  16. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

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  17. The number of faces of a triangular pyramid or tetrahedron is .

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  18. The acute angle that the vector 2hati-2hatj+hatk makes with the plane ...

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  19. If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2...

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  20. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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