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for any four vectors veca,vecb, vecc and...

for any four vectors `veca,vecb, vecc and vecd` prove that `vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]`

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`vecd.(vecaxx(vecbxx (vecc xxvecd)))`
`= vecd.(vecaxx((vecb.vecd)vecc- (vecb.vecc)vecd)))`
`vecd. ((vecb.vecd)(veca xx vecc)- (vecb.vecc)(veca xxvecd))`
`=(vecb.vecd)(vecd.(vecaxxvecc))-(vecb.vecc)(vecd.(veca xx vecd))`
`(vecb.vecd) [vecdvecavecc]`
`(vecb.vecd) [veca vecc vecd]`
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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. If vecl,vecm,vecn are three non coplanar vectors prove that [vec vecm ...

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  3. if the volume of a parallelpiped whose adjacent egges are veca=2hati+3...

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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.(vecb...

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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 vecp, vecq , vecr denote vectors vecbxxvecc, vecc xx vecc xx veca, ...

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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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