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Let veca , vecb and vecc be vectors form...

Let `veca , vecb and vecc` be vectors forming right- hand triad . Let `vecP= (vecbxxvecc)/([vecavecb vecc]), vecq (vecc xx veca)/([veca vecb vecc])and vecr= (vecaxxvecb)/([veca vecb vecc]) If x cupR^(+)` then

A

3

B

2

C

1

D

0

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Let veca,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are vectors defined by the relations vecp= (vecbxxvecc)/([veca vecb vecc]), vecq= (veccxxveca)/([veca vecb vecc]), vecr= (vecaxxvecb)/([veca vecb vecc]) then the value of the expression (veca+vecb).vecp+(vecb+vecc).vecq+(vecc+veca).vecr . is equal to (A) 0 (B) 1 (C) 2 (D) 3

Let veca,vecb,vecc be non coplanar vectors and vecp= (vecbxxvecc)/([veca vecb vecc]), vecq= (veccxxveca)/([veca vecb vecc]), vecr= (vecaxxvecb)/([veca vecb vecc]) . What is the vaue of (veca-vecb-vecc).vecp+(vecb-vecc-veca).vecq+(vecc-veca-vecb).vecr? (A) 0 (B) -3 (C) 3 (D) -9

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'vecb' and vecc' be its reciprocal set. prove that veca=(vecb'xxvecc')/([veca'vecb'vecc']),vecb=(vecc'xxveca')/([veca'vecb'vecc'])andvecc=(veca'xxvecb')/([veca'vecb'vecc'])

If veca,vecb,vecc be non coplanar vectors and vecp=(vecbxxvecc)/([veca vecb vecc]) , vecq=(veccxxveca)/([veca vecb vecc]) , vecr=(vecaxxvecb)/([veca vecb vecc]) then (A) vecp.veca=1 (B) vecp.veca+vecq.vecb+vecr.vecc=3 (C) vecp.veca+vecq.vecb+vecr.vecc=0 (D) none of these

veca, vecb,vecc are non-coplanar vectors and vecp,vecq,vecr are defined as vecp = (vecb xx vecc)/([vecb vecc veca]),q=(vecc xx veca)/([vecc veca vecb]), vecr =(veca xx vecb)/([veca vecb vecc]) then (veca + vecb).vecp+(vecb+vecc).vecq + (vecc + veca).vecr is equal to.

[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb vecc ] , then

If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecb xx vecc))/(vecb.(vecc xx veca)) + (vecb.(vecc xx veca))/(vecc.(veca xx vecb)) +(vecc.(vecb xx veca))/(veca. (vecb xx vecc)) is equal to:

If vecaxx(vecaxxvecb)=vecbxx(vecbxxvecc) and veca.vecb!=0 , then [(veca,vecb,vecc)]=

If [veca vecb vecc]=1 then value of (veca.vecbxxvecc)/(veccxxveca.vecb)+(vecb.veccxxveca)/(vecaxxvecb.vecc)+(vecc.vecaxxvecb)/(vecbxxvecc.veca) is

OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. Let a,b and c be distinct non-negative numbers. If the vectors ahati +...

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  2. If vecaxxvecb=vecc and vecbxxvecc=veca, show that veca,vecb,vecc are o...

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  3. Let veca , vecb and vecc be vectors forming right- hand triad . Let ve...

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  4. vecrxxveca=vecbxxveca,vecrxxvecb=vecaxxvecb,vecanevec0,vecbnevec0,veca...

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  5. The vector veca coplanar with the vectors hati and hatj perendicular t...

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  6. If the vectors veca and vecb are mutually perpendicular, then veca xx ...

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  7. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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  8. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  9. If the vectors (sec^(2)A)hati+hatj+hatk, hati+(sec^(2)B)hatj+hatk,hati...

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  10. x and y are two mutually perpendicular unit vector, if the vectors aha...

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  11. The three concurrent edges of a parallelopiped represent the vectors ...

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  12. If a=hati+hatj+hatk,b=hati+hatj,c=hati and (axxb)xxc=lamda a+mub, then...

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  13. If veca=2hati-3hatj+5hatk , vecb=3hati-4hatj+5hatk and vecc=5hati-3hat...

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  14. If veca,vecb,vecc are linearly independent vectors, then ((veca+2vecb)...

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  15. If veca,vecb are non-collinear vectors, then [(veca,vecb,hati)]hati+[...

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  16. If [(2veca+4vecb,vecc,vecd)]=lamda[(veca,vecc,vecd)]+mu[(vecb,vecc,vec...

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  17. If the volume of the tetrahedron whose vertices are (1,-6,10),(-1,-3,7...

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  18. (vecbxxvecc)xx(veccxxveca)=

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  19. When a right handed rectangular Cartesian system OXYZ is rotated about...

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  20. Prove that vectors vecu=(al+a(1)l(1))hati+(am+a(1)m(1))hatj + (an+a(...

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