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If vecr=x(1)(vecaxx vecb) + x(2) (vecb x...

If `vecr=x_(1)(vecaxx vecb) + x_(2) (vecb xxvecc) + x_(3)(vecc xxveca) and 4[veca vecb vecc] =1 " then " x_(1) + x_(2) + x_(3)` is equal to

A

`1/2vecr.(veca + vecb + vecc)`

B

`1/4vecr.(veca + vecb + vecc)`

C

`2vecr.(veca + vecb + vecc)`

D

`4vecr.(veca + vecb + vecc)`

Text Solution

Verified by Experts

The correct Answer is:
d
`vecr= x_(1)(vecaxx vecb) + x_(2)(vecb xx vecc)+x_(3)(vecc xxveca)`
`Rightarrow vecr.veca=x_(2)[veca vecb vecc] . vecr.vecb=x_(3)[vecb vecc veca]`
` and vecr.vecc= x_(1)[vecc veca vecb] =x_(1) [vecb vecc veca]`
` Rightarrow x_(1)+x_(2)+x_(3)=4vecr. (veca +vecb+vecc)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxv...

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

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

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  5. If veca' = hati + hatj, vecb'= hati - hatj + 2hatk nad vecc' = 2hati -...

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

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  7. If unit vectors veca and vecb are inclined at an angle 2 theta such th...

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  8. Differentiate y=cos^4 4x

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

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  10. If vectors veca and vecb are two adjacent sides of parallelograsm then...

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

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

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  13. 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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  14. If veca and vecb are two vectors and angle between them is theta , the...

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  15. Let veca and vecb are two given perpendicular vectors, which are non-z...

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  16. If vectors vecb= (tan alpha, -1,2 sqrtsinalpha//2)and vecc= (tanalpha,...

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

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

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

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  20. If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|v...

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