1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    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:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...