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Let veca, vecb, vecc be three non-coplan...

Let `veca, vecb, vecc` be three non-coplanar vectors and `vecp,vecq,vecr` be the vectors defined by the relations.
`vecp=(vecbxxvecc)/([(veca, vecb, vecc)]),vecq=(veccxxveca)/([(veca, vecb, vecc)]),vecr=(veccxxveca)/([(veca,vecb,vecc)])`
Then the value of the expression
`(veca+vecb).vecp+(vecb+vecc).vecq+(vecc+veca).vecr` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
NA
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. For any vectors vecr the value of hatixx(vecrxxhati)+hatjxx(vecrxxha...

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  2. If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, v...

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  3. Let veca, vecb, vecc be three non-coplanar vectors and vecp,vecq,vecr ...

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  4. If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecbxxvecc))...

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  5. Let veca=a(1)hati+a(2)hatj+a(3)hatk, vecb=b(1)hati+b(2)hatj+b(3)hatk a...

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  6. If the non zero vectors veca and vecb are perpendicular to each other,...

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  7. Prove that: [(vecaxxvecb)xx(vecaxxvecc)].vecd=pveca vecb vecc](veca.ve...

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  8. If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) then

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  9. If veca,vecb,vecc and vecp,vecq,vecr are reciprocal system of vectors,...

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  10. vecaxx(vecaxx(vecaxxvecb)) equals

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  11. If veca=hati+hatj-hatk, vecb=hati-hatj+hatk and vecc is a unit vector ...

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  12. If veca, vecb, vecc are non-coplanar unit vectors such that vecaxx(vec...

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  13. Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj...

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  14. If vecaxxvecb=vecc and vecbxxvecc=veca then a. veca,vecb,vecc are ort...

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  15. If vecp=(vecbxxvecc)/([(veca,vecb,vecc)]),vecq=(veccxxveca)/([(veca,ve...

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  16. If vecrxxveca=vecbxxveca,vecrxxvecb=vecaxxvecb,veca!=0,vecb!=0,veca!=l...

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  17. The vector veca coplanar with the vectors hati and hatj perendicular t...

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  18. If the vectors veca and vecb are mutually perpendicular, then vecaxx{v...

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  19. [((vecaxxvecb)xx(vecbxxvecc),(vecbxxvecc)xx(veccxxveca),(veccxxveca)xx...

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  20. Let veca=hati-hatj,vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit v...

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