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show that (vecaxxvecb)xxvecc=vecaxx(vecb...

show that `(vecaxxvecb)xxvecc=vecaxx(vecbxxvecc)` if and only if `veca and vecc` are collinear or `(vecaxxvecc)xxvecbxxvec0`

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we are given that
`(veca.vecc) vecb-(vecb.vecc)veca=(veca.vecc)vecb - (veca.vecb) vecc`
`(veca.vecb)vecc-(vecb.vecc)veca=vec0`
`Rightarrow (vecaxxvecc) xxvecb=vec0`
Thus , either , `vecb =vec0 or veca xx vecc = vec0`
But `vecb ne vec0` therefore, `veca xx vecc =vec0` and hence
`vecc = t veca ,, i.e. veca and vecc` are collinear.
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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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