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If vecb is a unit vector, then (veca. ve...

If `vecb` is a unit vector, then `(veca. vecb)vecb+vecbxx(vecaxxvecb)` is a equal to

A

`|veca|^(2)vecb`

B

`(veca.vecb)veca`

C

`veca`

D

`(veca. vecb)vecb`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`|vecb|=1`
`:.(veca.vecc)vecb+vecbxx(vecaxxvecb)`
`=(veca.vecb)vecb+|vecb|^(2)veca-(vecb.veca)vecb=(veca.vecb)vecb+veca-(veca.vecb)vecb=veca`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. If vecr is a unit vector such that vecr=x(vecbxxvecc)+y(veccxxveca)+...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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