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Simple vector proof?

  1. Nov 1, 2006 #1
    a is a vector and s and t are two integers. i'm supposed to show that:

    sa+ta=(s+t)a

    and

    s*(ta)=(s*t)a

    the two are so obvious i'm not sure how i prove them.
     
  2. jcsd
  3. Nov 1, 2006 #2

    arildno

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    Make a careful check of the axioms given for your vector space, and see what needs to be proven.
     
  4. Nov 1, 2006 #3
    thing is, i think i'm supposed to show it geometrically by drawing it. how do i do that?
     
  5. Nov 1, 2006 #4
    let a = (x,y) in the component form
    then
    sa+ta =
    s(x,y) + t(x,y) =
    (sx,sy) + (tx,ty)=
    (sx+tx,sy+ty)=

    (x(s+t),y(s+t))=

    (s+t)(x,y)=
    (s+t)a and do the similar for b)
     
  6. Nov 1, 2006 #5

    arildno

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    Well, sa is parallell to a, isn't it?
    And so is ta..
    So, how would you geometrically add these vectors, and what resultant vector does this equal?
     
  7. Nov 1, 2006 #6
    (s+t)*a

    but that is what i'm supposed to show. so is it enough to just draw sa and then ta from where sa ends? add them together so to speak?
     
  8. Nov 1, 2006 #7

    arildno

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    I guess so.
     
  9. Nov 1, 2006 #8

    Office_Shredder

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    That's about as geometrically proven as it gets....
     
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