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The position vectors of three A,B, and C...

The position vectors of three A,B, and C in space are respectively `2 vec i + 3 vec j - vec k, vec i - 2 vec j + 3 vec k` and `4 vec i + vec j + vec k`. Find the volume of the parallelepiped whose three concurrent edges are OA, OB and OC where O is the origin.

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A DAS GUPTA-Product of three or more Vectors-Exercise
  1. The position vectors of three A,B, and C in space are respectively 2 v...

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  2. If three concurrent edges of a parallelopiped of volume V represent ve...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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