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Value of [ vec axx vec b vec axx vec c v...

Value of `[ vec axx vec b vec axx vec c vec d]` is always equal to `( vec a . vec d)[ vec a vec b vec c]` b. `( vec a . vec c)[ vec a vec b vec d]` c. `( vec a . vec b)[ vec a vec b vec d]` d. none of these

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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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca, vecb and vecc are such that [veca vecb vecc] =1, vecc= lambda...

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  2. If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)...

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  3. Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec...

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  4. Let vec aa n d vec b be mutually perpendicular unit vectors. Then f...

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

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

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  9. If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

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  10. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

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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 aedn vecy: vecx+vec...

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  17. The condition for equations vec rxx vec a= vec ba n d vec rxx vec c...

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  18. If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2h...

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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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