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Find veca.vecb if |veca|2, |vecb|=5,a an...

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

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`veca.vecb= |veca||vecb|costheta,but |vecaxxvecb|=|veca||vecb|sintheta`
` or sin theta (|veca xx vecb|)/(|veca||vecb|)= 4/5 Rightarrow 4/5 Rightarrow theta= 3/5`
thereforem , `veca.vecb= 2xx5xx 3/5 = 6`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If A ,B ,C ,D are four distinct point in space such that A B is not...

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

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

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

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

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  6. I the vectors veca,veca=xhati+yhatj+zhatka and vecb=hatj are such that...

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  7. given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca...

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  8. Show that (veca-vecb)xx(veca+vecb)=2vecaxx vecb and give a genometrica...

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  9. If vec x and vecy are unit vectors and |vecz| = 2/sqrt7 such that vecz...

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

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

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

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

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

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

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

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

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

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

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

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