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In any triangle A B C , prove the projec...

In any triangle `A B C ,` prove the projection formula`a=b cosC+ccosB` using vector method.

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Let ` vecBC=veca, vecCA=vecb, vecAB=vecc`, so that
BC=a, CA =b,AB=c
`Now" " veca+vecb+vecc=vec0`
`veca.(veca+vecb+vecc)=0`
`veca.veca+veca.vecb+vecc=0`
`a^(2)+ab cos ( 180^(@)-C)+ac cos ( 180^(@)-B)=0`
`a-b cosC-c cosB=0`
`a=b cos C +c cos B`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. In any triangle A B C , prove the projection formulaa=b cosC+ccosB ...

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  2. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|...

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  3. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|v...

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  4. If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2...

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  5. If |veca|=3, |vecb|=4 and the angle between veca and vecb is 120^(@) ....

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  6. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

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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 find the ang...

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  9. If the angle between unit vectors veca and vecb is 60^(@) . Then find ...

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  10. Let vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn is...

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  11. A , B , C , D are any four points, prove that vec A Bdot 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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  13. If the vectors 3vecP+vecq, 5vecP - 3vecq and 2 vecp+ vecq, 4 vecp - 2v...

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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. Let veca , vecb and vecc be unit vectors such that veca+vecb+vecc=vecx...

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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 P(1)=hati-hatj+hatk, P(2)= -hati+2hatj-hatik and P(3)=...

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  18. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |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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  21. Find veca.vecb if |veca|2, |vecb|=5,a and |vecaxxvecb|=8

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