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Question on Vectors and Components (NOT HW)

  1. May 20, 2009 #1
    Okay, let's say theres vector a,b and c

    What would be the difference between


    projection of c on a and b

    and

    components of c along a and b


    I thought they were the same...

    thanks.
     
  2. jcsd
  3. May 20, 2009 #2
    The projections are like putting c and a or b tail to tail and dropping a perpendicular from the tip of c to the line defined by a or b and measuring from the tail of a or b to the intersection. In an inner product space with inner product <.,.>, the projection onto b can be calculated by <b, c>/||b||.
    The components of c with respect to a and b are the numbers ca and cb such that c = caa + cbb. In the case that c is the sum of a and b, the components with respect to a and b are (1, 1). By the parallelogram law, this obviously does not correspond to the projection unless a and b are orthogonal unit vectors.
     
  4. May 20, 2009 #3
    hmm... but drawing wise, they are the same?
     
  5. May 22, 2009 #4

    chiro

    User Avatar
    Science Advisor

    Drawing wise they should be the same as saying what the poster above said by
    grabbing the vector a and the vector c (we are projecting a onto c in this case) and its just the length of a in the c direction.

    With regards to your question i'm pretty sure you have the right idea.
     
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