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If veca=2hati+ 3hatj-5hatk,vecb =m hati+...

If `veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vecb = vec0` then find (m,n)

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`vecaxxvecb= |{:(hati ,hatj ,hatk),(2,3,-5),(m,n,12):}|`
` = (36 + 5n) hati - (24 - 5m) hatj + ( 2n - 3m) hatk`
`= vec0`
`m= (-24)/5 , n = (-36)/5`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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