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[( vec axx vec b)xx( vec bxx vec c)( vec...

`[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)]` is equal to (where ` vec a , vec ba n d vec c` are nonzero non-coplanar vector) a. `[ vec a vec b vec c]^2` b. `[ vec a vec b vec c]^3` c. `[ vec a vec b vec c]^4` d. `[ vec a vec b vec c]`

A

` [veca vecb vecc] ^(2)`

B

`[veca vecb vecc] ^(3)`

C

`[veca vecb vecc] ^(4)`

D

`[veca vecb vecc]`

Text Solution

Verified by Experts

The correct Answer is:
c
`[(vecaxxvecb)xx(vecbxxvecc) (vecbxxvecc) xx (vecc xxveca) (veccxxveca) xx (vecaxxvecb)]`
` [[veca vecb vecc]vecb [veca vecb vecc] vecc [veca vecb vecc] . Veca]`
`[veca vecb vecc]^(3)[vecbvecc veca] = [veca vecb vecc] ^(4)`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is ...

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  2. If V be the volume of a tetrahedron and V ' be the volume of another...

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  3. [( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)(...

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  4. If vecr=x(1)(vecaxx vecb) + x(2) (vecb xxveca) + x(3)(vecc xxvecd) and...

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  5. If the vectors veca and vecb are perpendicular to each other then a ve...

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  6. If veca' = hati + hatj, vecb'= hati - hatj + 2hatk and vecc' = 2hati -...

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  7. If veca= hati +hatj, vecb= hatj + hatk, vecc = hatk + hati then in th...

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  8. If unit vectors vec a and vec b are inclined at angle 2theta such t...

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  9. vec a, vec ba n d vec c are non-collinear if vec axx( vec bxx vec c)+...

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  10. Let vec adot vec b=0,w h e r e vec aa n d vec b are unit vectors and ...

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  11. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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  12. If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec...

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  13. If vecp=(vecbxxvecc)/([(veca,vecb,vecc)]),vecq=(veccxxveca)/([(veca,ve...

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  14. a(1), a(2),a(3) in R - {0} and a(1)+ a(2)cos2x+ a(3)sin^(2)x=0 " for ...

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  15. If vec aa n d vec b are two vectors and angle between them is thet...

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  16. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

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  17. If vector vec b=(t a nalpha,-1, 2sqrt(sinalpha//2))a n d vec c=(t a n...

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  18. Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |v...

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  19. If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ ...

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  20. If veca and vecb are two unit vectors perpenicualar to each other and ...

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