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If three concurrent edges of a parallelo...

If three concurrent edges of a parallelopiped of volume `V` represent vectors `veca,vecb,vecc` then the volume of the parallelopiped whose three concurrent edges are the three concurrent diagonals of the three faces of the given parallelopiped is

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The three concurrent edges of a parallelopiped represent the vectors veca, vecb, vecc such that [(veca, vecb, vecc)]=V . Then the volume of the parallelopiped whose three concurrent edges are the three diagonals of three faces of the given parallelopiped is

The three concurrent edges of a parallelopiped represents the vectors bar(a),bar(b),bar(c) such that [bar(a)bar(b)bar(c)]=lambda. Then the volume of the parallelopiped whose three concurrent edges are the threeconcurrent diagonals of three faces of the given parallelopiped is-

Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

If the volume of a parallelopiped whose three coterminal edges are represented by vectors, then lambda =________.

The volume of a parallelopiped whose coterminous edges are 2veca , 2vecb , 2 vec c , is

If [veca vecbvecc]=2 find the volume of the parallelepiped whose co-teminus edges are 2veca +vecb, 2 vecb + vecc, 2 vecc + veca.

The volume of the parallelopiped constructed on the diagonals of the faces of the given rectangular parallelopiped is m times the volume of the given parallelopiped. Then m is equal to

Volume of parallelopiped formed by vectors vecaxxvecb, vecbxxvecc and veccxxveca is 36 sq.units, then the volume of the parallelopiped formed by the vectors veca,vecb and vecc is.

Find the volume of the parallelopiped whose thre coterminus edges asre represented by veci+vecj+veck, veci-vecj+veck,veci+vec(2j)-veck .

A DAS GUPTA-Product of three or more Vectors-Exercise
  1. If three concurrent edges of a parallelopiped of volume V represent ve...

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  2. The position vectors of the points A,B,C , D are respectively 2 vec i ...

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  3. If the three vectors vec a+ vec b , vec b+ vec c and vec c+ vec a ar...

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  4. Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

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  5. Let vec a = a1 hat i + a2 hat j+ a3 hat k;vec b = b1 hat i+ b2 hat j+...

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  6. lf vec a,vec b,vec c , vec a', vec b',vec c', are two sets of non-...

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  7. Let vec(a),vec(b)andvec(c) be three non-coplanar vectors and let vec(p...

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  8. If vec a,vec b,vec c are three vectors such that vec a+vec b+vec c=vec...

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  9. Prove that hat ixx( vec axx hat i) hat jxx( vec axx hat j)+ hat kxx( ...

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  10. If vecaxx(vecbxxvecc)+(veca*vecb)vecb=(4-2beta-sinalpha)vecb+(beta^2-...

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  11. Let vec abe a unit vector and vec ba non-zero vector not parallel to v...

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  12. For any vector vec a , prove that | vec axx hat i|^2+| vec axx hat j|...

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  13. If vectors b ,ca n dd are not coplanar, then prove that vector ( ve...

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  14. If vec a, vecb and vec c are three conterminuous edges of a parallelo...

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  15. Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equal...

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  16. If vec a=vec i + vec j + vec k, vec b=vec i - vec j + vec k and vec c=...

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  17. If the volume of a parallelopiped, whose three coterminous edges are -...

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  18. Find the volume of the parallelepiped whose coterminous edges are r...

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  19. The points (3,6,9), (1,2,3), (2,3,4) and (4,6,lambda) are coplanar if ...

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  20. If vec xdot vec a=0, vec xdot vec b=0a n d vec xdot vec c=0 for some ...

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