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Let vec a , vec b ,a n d vec c be non-c...

Let ` vec a , vec b ,a n d vec c` be non-coplanar vectors and let the equation ` vec a^' , vec b^' , vec c '` are reciprocal system of vector ` vec a , vec b , vec c ,` then prove that ` vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c '` is a null vector.

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`veca xx veca' = (veca xx (vecb xx vecc))/([veca vecb vecc])= (veca.vecc)vecb - (veca .vecb)vecc)/([veca vecb vecc]) `
similarly, `vecb xx veb' = ((vecb .veca)vecc- (vecc.vecc)veca)/[veca vecb vecc] `
`and vecc xx vecc' = ((vecc. Vecb) veca - (veca .veca) vecb)/[veca vecb vecc]`
so `vecaxx veca'+vecbxxvecb' +veccxxvecc' =0`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.3
  1. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

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  2. If vecl,vecm,vecn are three non coplanar vectors prove that [vec vecm ...

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  3. If the volume of a parallelepiped whose adjacent edges are vec a=2...

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  4. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

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  5. If vecx . Veca =0, vecx. Vecb=0 and vecx. vecc=0 for some non-zero vec...

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  6. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

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  7. If vec a , vec b, and vec c are three vectors such that vec axx ve...

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  8. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove...

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  9. Prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vec...

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  10. For any four vectors, vec a , vec b , vec c and vec d prove that vec...

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  11. If vec a and vec b be two non-collinear unit vector such that vec ...

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  12. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

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  13. If vec a , vec b , and vec c be non-zero vectors such that no two ...

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  14. If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a...

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  15. Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the...

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  16. Given unit vectors hatm hatn and hatp such that angle between hatm and...

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  17. vec a , vec b ,a n d vec c are three unit vectors and every two are...

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  18. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

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