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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)xxvecb=vec0`

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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 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. prove that if [vecl vecm vecn] are three non-coplanar vectors, then [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=0 vecx.vecb=0 and vecx.vecc=0 for some non zero vector ve...

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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,vecc are three non-coplanar vectors such that veca xx 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. Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)x...

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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 hat m , hat n and hat p such that angel between h...

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  17. veca,vecb, vecc are threee unit vectors and every two are two inclined...

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

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