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Sholve the simultasneous vector equation...

Sholve the simultasneous vector equations for `vecx and vecy: vecx+veccxxvecy=veca and vecy+veccxxvecx=vecb, vecc!=0`

A

`vecx=(vecbxxvecc+veca+(vecc.veca)vecc)/(1+ vecc.vecc)`

B

`vecx=(veccxxvecb+vecb+(vecc.veca)vecc)/(1+vecc.vecc)`

C

`vecy=(vecaxxvecc+vecb+(vecc.vecb)vecc)/(1+vecc.vecc)`

D

none of these

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Verified by Experts

The correct Answer is:
b
`vecx +vecc xx vecy = veca`
`vecy +vecc xx vecx =vecb`
taking cross with `vecc` , we have
`vecc xx vecy + vecc xx (vecc xx vecx) =vecc xx vecb`
` Rightarrow (veca - vecx) + (vecc .vecx)vecc- (vecc.vecc)vecx = vecc xx vecb`
Also `vecx + vecc xx vecy= veca`
` Rightarrow vecc. vecx + vecc.(vecc xx vecy) =vecc. veca`
` or vecc . vecx + 0 = vecc.vcea`
` Rightarrow veca- vecx + (vcec - veca) vecc -(vecc-vecc)vecx = vecc xx vecb`
`or vecx ( 1 + (vecc.vecc)) = vecb xx vecc + veca + (vecc .veca). vecc`
`or vecc= (vecb xx vecc + veca + (vecc . vecb) vecc)/ (1+vecc.vecc)`
similarly on taking cross product of Eq (i) , we find
` vecy = (veca xx vecc + vecb + (vecc. veca) vecc)/ (1 + vecc .vecc)`
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CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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  2. If veca+vecb ,vecc are any three non- coplanar vectors then the equa...

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  3. Sholve the simultasneous vector equations for vecx and vecy: vecx+vecc...

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  4. The condition for equations vecrxxveca = vecb and vecr xx vecc = vecd ...

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

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  6. If veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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

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

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

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

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

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

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

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  14. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca)...

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

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

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

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

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

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  20. vecb and vecc are non- collinear if veca xx (vecb xx vecc) + (veca .ve...

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