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If veca,vecb,vecc are unit vectors such ...

If `veca,vecb,vecc` are unit vectors such that `veca+vecb+vecc=vec0` , find the value of `veca*vecb+vecb*vecc+vecc*veca`.

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squaring `(veca+vecb+vecc)= vec0` we get
`|veca|^(2)+|vecb|^(2)=|vecc|^(2)+2 veca.vecb+ 2vecb.vecc + 2vecc.veca=0`
`2(veca.vecb+vecb.vecc+vecc.veca)=-3`n
`veca.vecb+vecb.vecc+vecc.veca= -3/2`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  4. If the vertices A,B, C of a triangle ABC are (1,2,3),(-1, 0,0), (0, 1,...

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  7. Let veca vecb and vecc be pairwise mutually perpendicular vectors, suc...

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  8. If veca+vecb+vecc =0, |veca|=3, |vecb|=5, |vecc|=7 then the angle betw...

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  11. A , B , C , D are any four points, prove that vec A B dot vec C D+ ...

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  12. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection...

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  14. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

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  15. If veca ,vecb, vec c are three vectors such that veca + 2 vecb + vecc ...

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  16. If veca and vecb are unit vectors, then find the greatest value of |ve...

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  17. Constant forces P1= hat i+ hat j+ hat k ,P2= hat i+2 hat j- hat ka n d...

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  18. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

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  19. If A ,B ,C ,D are four distinct point in space such that A B is not...

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  20. If veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vec...

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