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How to prove this without computation

  1. Apr 12, 2015 #1
    1. The problem statement, all variables and given/known data
    Prove: In R3if a and b are orthogonal vectors, then for every nonzero vector u, we have proja(projbu)=0

    2. Relevant equations
    I know the dot product of a and b is zero

    3. The attempt at a solution

    Based on the definition of projection I eventually got to
    (ab) in the numerator which is zero and was done. So how can I write this out with words only?
     
  2. jcsd
  3. Apr 12, 2015 #2

    LCKurtz

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    You haven't defined projbu but I suppose it is the projection on b of u. I'm not sure why you want to write it "in words" instead of equations, but you could observe that the projection on b of u is a multiple of b. Then since a is orthogonal to b, then....
     
  4. Apr 12, 2015 #3
    then that component is zero? Yeah I will add the computation also but I wasn't really sure what else to say.

    yeah its the projection on b of u
     
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