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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)=8and|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. If |veca|=2, |vecb|=5 and |vecaxxvecb|=8 then find the value of veca.v...

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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. if the vectors vecc, veca = xhati +yhatj + zhatk and vecb = hatj are s...

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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)=2(vecaxxvecb)

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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. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

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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. If veca,vecb,vecc be unit vectors such that veca.vecb=veca.vecc=0 and ...

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  15. if (vecaxxvecb)^(2)+ (veca.vecb)^(2) = 144 and |veca|=4 the find the v...

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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 vectors veca, vecb and vecc are coplanar, show that |{:(veca, vecb,...

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  20. If the volume of a parallelepiped whose adjacent edges are vec a=2...

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