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Another vector problem

  1. Sep 24, 2006 #1
    These vectors are giving me some real trouble...i'm fine with the in physics, but the math theory behind them is my weakness...

    Ok, so we have that u.v=u.w where those are dot products of vectors. The question asks whether or not it makes sense to equate that to meaning that v=w.

    Now, at first glance I would say yes. Since u never changes, for the dot product to be the same of the 2 expressions v and w would have to be the same vectors. But i have a strong feeling that i'm wrong...seems like one of those questions designed to make you second-guess yourself.

    Any pointers on how to work this one out would be appreciated
     
  2. jcsd
  3. Sep 24, 2006 #2
    Hint: Dot product is commutative. :smile:
     
  4. Sep 24, 2006 #3
    hmmm, yes, i knew that; but i'm not entirely sure as to how that helps. It only seems to further my belief that v=w...which is possible i guess; maybe i'm overthinking it.

    the way i see it is that if

    u.v = u.w and
    u.v = v.u

    all that means is that v.u = u.w

    and that doesn't get me any further to understanding :(
     
  5. Sep 24, 2006 #4

    matt grime

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    u.v=u.w is the same as saying u.(v-w)=0. Now is it true that for all u, u.z=0 means z equals zero?
     
  6. Sep 24, 2006 #5
    As far as I know, no; that doesn't mean z=0. So v-w wouldn't have to be zero, meaning they're not equal :)

    Thanks a lot! The commutativity hint was received poorly on my part, i never even considered taking u.w to the other side...
     
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