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Given | vec a|=| vec b|=1a n d| vec a+ v...

Given `| vec a|=| vec b|=1a n d| vec a+ vec b|=3.` If ` vec c` is a vector such that ` vec c- vec a-2 vec b=3( vec axx vec b),` then find the value of ` vec cdot vec bdot`

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A DAS GUPTA-Product of three or more Vectors-Exercise
  1. Prove that hat ixx( vec axx hat i) hat jxx( vec axx hat j)+ hat kxx( ...

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

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

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

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

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

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

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

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

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

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

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

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  13. Let veca,vecb and vecc be three vectors having magnitudes 1, 1 and 2 r...

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  14. The scalar vec Adot( vec B+ vec C)xx( vec A+ vec B+ vec C) equals 0 b...

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  15. Let a,b,c be distinct non zero numbers. If the vectors a vec i + a ve...

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  16. The vectors vecaxx(vecbxxvecc), vecbxx(veccxxveca) and veccxx(vecaxxve...

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  17. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  18. In each of the following, one or more options ar correct. Choose the ...

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  19. If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then ...

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  20. Given | vec a|=| vec b|=1a n d| vec a+ vec b|=3. If vec c is a vector...

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