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A , B , C , D are any four points, prove...

`A , B , C , D` are any four points, prove that ` vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.`

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`vec(AD)=vec(AB)+vec(BC)+vec(CD)=veca+vecb+vecc`
`vec(AC)=vec(AB)+vec(BC)=veca+vecborvec(CA)=-(veca+vecb)`
`vec(BD)=vec(BC)=vec(CD)=vecb+vecc`
`vec(AB).vec(CD)+vec(BC).vec(AD)+vec(CA).vec(BD)`
`veca.vecc+vecb.(veca+vecb+vecc)+(=-veca-vecb).(vecb+vecc)`
`= veca.vecc+vecb.veca+vecb.vecb+vecb.vecc-veca.vecb-veca.vecc`
`-vecb.vecb-vecb.vecc=0`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  6. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

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

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

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

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

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  13. Find veca.vecb if |veca|2, |vecb|=5,a and |vecaxxvecb|=8

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  14. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

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  15. If veca = 2vecj+3vecj-veck, vecb =-veci+2vecj-4veck and vecc=veci + ve...

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