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Dot product

  1. Sep 22, 2003 #1
    How do you expand and simplify this one?


    (2u+v).(u-2v)
    =2u.u+2u.(-2v)+v.u+v.(-2v)

    Where u and v are vectors and the "." is the dot. I did some but after this im lost, how can I continue?
     
  2. jcsd
  3. Sep 22, 2003 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I don't see what your problem is. You have done
    (2u+v).(u-2v)=2u.u+2u.(-2v)+v.u+v.(-2v) correctly. Now just
    combine 2u.(-2v)= -4 u.v and v.u which is also u.v:
    This is 2(u.u)- 3 u.v- 2(v.v)

    You can also use the fact that |u|= sqrt(u.u) so that
    u.u= |u|2 and v.v= |v|2 so that
    (2u+v).(u-2v)= |u|2- 3u.v- 2|v|2.
     
  4. Sep 23, 2003 #3
    Got it, thanks :smile:
     
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