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(vecaxxvecb).(veccxxvecd) is not equal t...

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

A

`veca.{vecbxx(veccxxvecd)}`

B

`{(vecaxxvecb)xxvecc}vecd`

C

`(vecd xx vecc).(vecbxxveca)`

D

`(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc)`

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly
`(vecaxxvecb).(veccxxvecd)={(vecaxxvecbxxvecc)}.vecd`
`implies(vecaxxvecb).(veccxxvecd)={(vecc.veca)vecb-(vecc.vecb)veca}.vecd`
`implies(vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc)`
Also we have
`(vecaxxvecb).(veccxxvecd)=veca.{vecbxx(veccxxvecd)}`
and `(vecaxxvecb).(veccxxvecd)=(vecd xx vecc).(vecbxxveca)`
Hence vector in option b is not equal to the given vector.
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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