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If veca,vecb and vecc are three non copl...

If `veca,vecb and vecc` are three non coplanar vectors and `vecr` is any vector in space, then `(vecaxxvecb)xx(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)=` (A) `[veca vecb vecc]` (B) `2[veca vecb vecc]vecr` (C) `3[veca vecb vecc]vecr` (D) `4[veca vecb vecc]vecr`

A

`[veca vecb vecc]vecr`

B

`2 [veca vecb vecc]vecr`

C

`3 [veca vecb vecc]vecr`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
` (veca xx vecb) xx (vecr xx vecc)`
`= ((veca xx vecb) .vecc) vecr- ((veca xx vecb).vecr) .vecc`
` [veca vecb vecc] vecr- [veca vecb vecr] vecc`
similarly, ` (vecb xx vecc) xx (vecr xx veca)`
`= [vecb vecc veca] vecr - [vecb vecc vecr] veca`
` and (vecc xx veca) xx (vecr xx vecb) = [vecc veca vecb] vecr - [vecc veca vecr] vecb`
` Rightarrow (veca xx vecb ) xx (vecr xx vecc) + (vecb xx vecc)`
`x (vecr xx veca) + (vecc xx veca0 xx (vecr xx vecb)`
` 3[ veca vecb vecc] vecr - ([vecb vecc vecr]veca + [vecc veca vecr] vecr + [veca vecb vecr] vecc)`
` 3[veca vecb vecc] vecr - [veca vecb vecc] vecr = 2 [veca vecb vecc] vecr`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Let veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati ...

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

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

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

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

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

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

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

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

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  10. If veca bot vecb then vector vecv in terms of veca and vecb satisfying...

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  11. If vec a^'= hat i+ hat j , vec b^' hat i- hat j+2 hat ka n d vec c^'2...

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

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

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

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  15. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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

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

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  18. Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. L...

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

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