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If veca .vecb =beta and veca xx vecb = v...

If `veca .vecb =beta and veca xx vecb = vecc ," then " vecb` is

A

`((betaveca-vecaxxvecc))/(|veca|^(2))`

B

`((betaveca+vecaxxvecc))/(|veca|^(2))`

C

`((betavecc + vecaxxvecc))/(|veca|^(2))`

D

`((betavecc + vecaxxvecc))/(|veca|^(2))`

Text Solution

Verified by Experts

The correct Answer is:
a
` veca xx vecb =vecc`
`or veca xx (veca xx vecb) =veca xx vecc `
`or (vec.vecb) veca - |veca|^(2) vecb = veca xx vecc`
`or vecvb = (betaveca -veca xx vecc)/(|veca|^(2) " " (veca .vecb = beta)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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  2. Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))...

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  3. If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

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  4. If a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec...

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  5. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

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  6. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  7. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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  8. If veca and vecb are two unit vectors inclined at an angle pi//3 then ...

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  9. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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  10. If veca+vecb ,vecc are any three non- coplanar vectors then the equa...

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  11. Sholve the simultasneous vector equations for vecx aedn vecy: vecx+vec...

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  12. The condition for equations vecrxxveca = vecb and vecr xx vecc = vecd ...

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  13. If veca=2hati + hatj + hatk,vecb=hati + 2hatj + 2hatk ,vecc= hati + ha...

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  14. If veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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  15. Let (veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati...

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  16. For any vectors veca and vecb, (veca xx hati) + (vecb xx hati) + ( vec...

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  17. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

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  18. If vecP = (vecbxxvecc)/([vecavecbvecc]).vecq=(veccxxveca)/([veca vecb ...

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  19. A (veca), B (vecb) and C (vecc) are the vertices of triangle ABC and R...

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  20. If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is ...

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