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Linear Algebra - Projection of Vector

  1. Apr 8, 2016 #1
    1. The problem statement, all variables and given/known data

    I feel like this is a easy question but it seems the answer key doesn't seem to be right.

    So say I have 2 vectors

    equation 1.PNG

    and I'm trying to find the projection of vector u perpendicular to the vector v

    2. Relevant equations


    3. The attempt at a solution

    So I don't remember doing something like this before but I would assume that I start off by finding the projection of u in direction of v

    equation 2.PNG
    alright so this gives me
    equation 3.PNG

    So conceptually thinking I see that I have a vector u and a vector V|| sort of like this

    IMG_20160408_153526779.jpg
    So I can find the angle between u and V and I get 104.963 degrees

    IMG_20160408_153856303.jpg

    So to get the perpendicular component is it just

    tan(theta) = (V perpendicular)/(V parallel)
    so V perpendicular is
    (V parallel)tan(theta) = V perpendicular?

    IMG_20160408_154414914.jpg

    I think is conceptually ok but I'm not sure because my answer key does V - V parallel which would appear to be wrong in my opinion because I don't see how that would give us V perpendicular, unless I'm not understanding what vector I'm looking for.

    Thanks for any help.
     
  2. jcsd
  3. Apr 8, 2016 #2
    I see that apparently the answer key is correct and see why never mind
     
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