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Let veca vecb and vecc be three non-zero...

Let `veca vecb and vecc` be three non-zero vectors such that `veca + vecb + vecc = vec0 and lambda vecb xx veca xx veca + vecbxxvecc + vecc + veca = vec0` then find the value of `lambda`.

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Clearly, `veca , vecb and vecc` respesent the sides of a tirangle,
`Rightarrow veca xx vecb =vecc xx veca `
`or veca xxvecb + vecc + vecb xx vecc xx veca = 3veca xx vecb`
`or 2vecb xx veca +vecb xx vecc + vecc xx veca = 0 Rightarrow lambda=2`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If vec x and vecy are unit vectors and |vecz| = 2/sqrt7 such that vecz...

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  2. prove that (veca.hati)(vecaxxhati)+(veca.hatj)(vecaxxhatj)+(veca.hatk)...

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  3. Let veca vecb and vecc be three non-zero vectors such that veca + vecb...

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  4. A particle has an angular speed of 3 rad/s and the axis of rotation...

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  5. Let vea, vecb and vecc be unit vectors such that veca.vecb=0 = veca.ve...

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  6. If |vecaxxvecb|^(2)+(veca.vecb)^(2)=144and|veca|=4,"then "|vecb| is eq...

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  7. Given |veca|=|vecb|=1 and |veca + vecb|= sqrt3 "if" vecc is a vector s...

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  8. Find the moment of vec F about point (2, -1, 3), where force vec ...

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  9. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

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

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

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  12. If veca=hati+hatj+hatk and vecb = hati-2hatj+hatk then find vector vec...

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  13. If vecx.veca=0vecx.vecb=0 and vecx.vecc=0 for some non zero vector vec...

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

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  15. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

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

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  17. prove that (veca.(vecbxxhati)hati(veca.(vecbxxhatj))hatj+ (veca.(vecbx...

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  18. for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecax...

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

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

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