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value of [vecaxxvecbvecaxxvecc vecd] is...

value of `[vecaxxvecbvecaxxvecc vecd]` is always equal to

A

`(veca.vecd) [vecavecbvecc]`

B

`(veca.vecc)[veca vecb vecd]

C

`(veca.vecb)[veca vecb vecd]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
` [veca xx vecb veca xx vecc vecd]`
`= (veca xx vecb) .(( veca xx vecc) xx vecd)`
` (veca xx vecb) . ((veca.vecd)vecc= (vecc.vecd) veca)`
` (veca.vecd) [veca vecb vecc]`
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For any four vectors veca, vecb, vecc, vecd the expressions (vecb xx vecc).(veca xx vecd) +(vecc xx veca).(vecb xx vecd)+(veca xx vecb).(vecc xx vecd) is always equal to:

[vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

[vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to (a) [veca vecb vecd] [vecc vece vecf]-[veca vecb vecc] [vecd vece vecf] (b) [veca vecb vece ] [vecf vecc vecd] - [veca vecb vecf] [vece vecc vecd] (c) [vecc vecd veca] [vecb vece vecf] - [veca vecd vecb] [vecavece vecf] (d) [veca vecc vece] [vecb vecd vecf]

CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If veca, vecb and vecc are such that [veca \ vecb \ vecc] =1, vecc= la...

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  2. If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxve...

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  3. value of [vecaxxvecbvecaxxvecc vecd] is always equal to

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  4. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

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  5. Let veca and vecb be unit vectors that are perpendicular to each other...

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  6. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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  7. If vecb and vecc are unit vectors, then for any arbitary vector veca,...

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

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

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  10. if (vecaxxvecb)xx(vecbxxvecc)=vecb, " where " veca, vecb and vecc are ...

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

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

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

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

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

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  16. Sholve the simultasneous vector equations for vecx and vecy: vecx+vecc...

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

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  18. If veca=2hati + hatj + hatk, vecb=hati + 2hatj + 2hatk then [veca vecb...

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

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

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