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prove that (veca.(vecbxxhati))hati+(veca...

prove that `(veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vecbxxhatk))hatk=vecaxxvecb`

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`veca.(vecbxx hati)hati = ((vecaxxvecb).hati)hati`
`if veca xx vecb = xhati + yhatj + zhatk , then (veca xx vecb). Hati = x `
similarly, `(veca. (vecb xx vecj)) hatj = y and (veca . (vecb xx veck)) =z `
`Rightarrow (veca.(vecb.hati)) hati+ (veca . vecb xx vecj)) hatj + (veca .(vecb xx veck)) hatk`
= xhati + y hatj = zhatk = veca xx vecb`
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CENGAGE-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. Prove that [veclvecmvecn][vecavecbvecc]=|{:(vecl.veca,vecl.vecb,vecl.v...

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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=0vecx.vecb=0 and vecx.vecc=0 for some non zero vector 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 veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

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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 veca,vecb, vecc and vecd prove that vecd. (vecax...

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  11. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

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

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  13. Let veca, vecb and vecc be non-zero vectors such that no two are colli...

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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 veca, vecb , vecc be non -coplanar vectors and let equations veca'...

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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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