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Prove that (veca.(vecbxxhati))hati+(veca...

Prove that `(veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vecbxxhatk))hatk=vecaxxvecb`

A

`2(vecaxxvecb)`

B

`3(vecaxxvecb)`

C

`vecaxxvecb`

D

`-(vecaxxvecb)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`{(veca.(vecbxxhati)}hati+{veca.(vecbxxhatj)}hatj+{veca.(vecbxxhatk)}hatk`
`={(vecaxxvecb).hati}hati+{(vecaxxvecb).hatj}hatj+{(vecaxxvecb).hatk}hatk`
`=vecaxxvecb [ :' vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk]`
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. If veca bot vecb then vector vecv in terms of veca and vecb satisfying...

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  2. Find the value of a so that the volume of the parallelopiped formed b...

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

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  4. If vecA , vecB and vecC are vectors such that |vecB| = |vecC| prove th...

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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 parallelopiped formed by the vectors a,b,c as three c...

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

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  9. Prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vec...

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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 (veca xx vecb) x...

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  12. vecp, vecq and vecr are three mutually prependicular vectors of the sa...

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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 A B C D are given by vec A B=...

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  15. Let a=hat(j)-hat(k) and b=hat(i)-hat(j)-hat(k). Then, the vector v sat...

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

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

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

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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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