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Simple Vector Component Projection

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the two vectors A=ai and B=3i+4j. What must be the value of a if the component of A along B is 6?


    2. Relevant equations



    3. The attempt at a solution

    I've arrived at the correct answer by finding the angle between the x component of B (3) and B itself which comes out to 53.13 degrees. Then 6/cos53.13 = 10 which is the correct result. However, I still don't understand what it means for something to be the component of A along B. I was hoping someone here could shed some light on what this means and how to visualize it.

    Thank you,
    Odd
     
  2. jcsd
  3. Sep 15, 2011 #2

    Hootenanny

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  4. Sep 15, 2011 #3

    BruceW

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    Hootenanny, do you mean scalar product? If so, then yeah, I agree. The sentence 'component of A along B' is simply the scalar product of the vectors A and the unit vector of B, ie B/ lBl.

    The scalar product can be written out in terms of the components of the two vectors as: (A1B1+A2B2+A3B3) / lBl (when the vectors are expressed in some orthogonal coordinate system).

    For a geometrical representation, the scalar product of A and the unit vector B / lBl is also equal to lAl cos(angle) where angle is the angle between those vectors.

    The intuitive way to think of 'the component of A along B' is that you simply look at the length of the vector A in the same direction as B.
     
    Last edited: Sep 15, 2011
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