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Value of `[ vec axx vec b , vec axx vec c , vec d]` is always equal to a. `( vec adot vec d)[ vec a vec b vec c]` b. `( vec adot vec c)[ vec a vec b vec d]` c. `( vec adot 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 PUBLICATION-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 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...

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

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  5. Let vec aa n d vec b be unit vectors that are perpendicular to each ...

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

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  10. If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ...

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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 vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

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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. Solve the simultaneous vector equations for vecx and vecy: vecx+veccxx...

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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 + 3hatj+ 8hatk is perpendicular to vecb= 4hati-4hatj + a...

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

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