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Let veca=hatj-hatk and vecc=hati-hatj-ha...

Let `veca=hatj-hatk` and `vecc=hati-hatj-hatk`. Then the vector `vecb` satisfying `vecaxxvecb+vecc=vec0` and `veca.vecb=3` is

A

`hati-hatj-2hatk`

B

`hati+hatj-2hatk`

C

`-hati+hatj-2hatk`

D

`2hati-hatj+2hatk`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`vecaxxvecb+vecc=vec0`
`impliesvecc=vecbxxveca`
`impliesvecaxxvecc=vecaxx(vecbxxveca)`
`impliesvecaxxvecc=(veca.veca)vecb-(veca.vecb)veca`
`implies-2hati-hatj-hatk=2vecb-3(hatj-hatk)`
`implies2.vecb=-2hati+2hatj-4hatkimpliesvecb=-hati+hatj-2hatk`
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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. If the vectors veca and vecb are perpendicular to each other then a ve...

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

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

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

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  5. If the magnitude of the moment about the pont hatj+hatk of a force hat...

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  6. If the volume of the parallelopiped formed by the vectors veca, vecb, ...

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  7. If |veca|=5, |vecb|=3, |vecc|=4 and veca is perpendicular to vecb and ...

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  8. If veca, vecb, vecc, vecd are coplanar vectors, then (vecaxxvecb)xx(ve...

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  9. {veca.(vecbxxhati)}hati+{veca.(vecbxxhatj)}hatj+{veca.(vecbxxhatk)}hat...

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  10. The unit vector which is orhtogonal to the vector 3hati+2hatj+6hatk an...

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  11. Let veca,vecb and vecc be non-zero vectors such that no two are collin...

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  12. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  13. If veca and vecb are vectors in space given by veca=(hati-2hatj)/(sqrt...

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  14. Two adjacent sides of a parallelogram ABCD are given by vec(AB)=2hati+...

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  15. Let veca=hatj-hatk and vecc=hati-hatj-hatk. Then the vector vecb satis...

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  16. The vector (s) which is (are) coplanar with vectors hati+hatj+2hatk an...

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  17. Let veca=-hati-hatk, vecb=-hati+hatj and vecc=hati+2hatj+3hatk be th...

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  18. If veca=1/(sqrt(10))(3hati+hatk),vecb=1/7(2hati+3hatj-6hatk), then the...

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  19. If veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk and vecc=rhati+hatj+(2...

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  20. If veca, vecb are non zero vectors, then ((vecaxxvecb)xxveca).((vecbxx...

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