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If veca, vecb, vecc are three non colana...

If `veca, vecb, vecc` are three non colanar, non =null vectors, and `vecr` is any vector in space, then
`(vecaxxvecb)xx(vecrxxvecc)+(vecbxxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)` is equal to

A

`2[(veca, vecb, vecc)]vecr`

B

`3[(veca, vecb, vecc)]vecr`

C

`[(veca, vecb, vecc)]vecr`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`(vecaxxvecb)xx(vecrxxvecc)=[(veca, vecb, vecc)]vecr-[(veca, vecb, vecr)]vecc`
`(vecbxxvecc)xx(vecrxxveca)=[(vecab, vecc, veca)]vecc-[(vecb, vecc, vecr)]veca`
`(veccxxveca)xx(vecrxxvecc)=[(vecc, veca, vecb)]vecr-[(vecc, veca, vecr)]vecb`
`:.(vecaxxvecb)xx(vecrxxvecc)+(vecbxxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)`
`=3[(veca, vecb, vecc)]vecr-[(veca, vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb`
`=3[(veca, vecb, vecc)]vecr=[(veca, vecb, vecc)]vecr=2[(veca, vecb, vecc)]vecr`.
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. (vecaxxvecb).(veccxxvecd) is not equal to

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  2. Let veca=2hati+hatj-2hatk and vecb=hati+hatj. If vecc is a vector such...

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  3. If veca, vecb, vecc are three non colanar, non =null vectors, and vecr...

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  4. The acute angle betwene any two faces of a regular tetrahedron is

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

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

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  7. The three vectors hati+hatj, hatj+hatk, hatk+hati taken two at a time ...

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  8. Let G(1),G(2),G(3) be the centroids of the triangular faces OBC, OCA, ...

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  9. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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  10. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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  11. If veca and vecb are two unit vectors, then the vector (veca+vecb)xx(v...

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  12. If vec(alpha)=2hati+3hatj-hatk, vec(beta)=-hati+2hatj-4hatk, vecgamma=...

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  13. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  14. Given |veca|=|vecb|=1 and |veca+vecb|=sqrt(3). If vecc be a vector suc...

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  15. If vecu and vecv be unit vectors. If vecw is a vector such that vecw+(...

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  16. If veca, vecb, vecc be three vectors of magnitude sqrt(3),1,2 such tha...

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  17. If the vectors veca and vecb are perpendicular to each other then a ve...

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  18. The value of a so that the volume of the paralelopiped formed by hati+...

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  19. Let veca, vecb and vecc be three vectors having magnitudes 1,1 and 2 r...

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  20. If veca, vecb, vecc are vectors such that |vecb|=|vecc| then {(veca+ve...

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