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Multivariable Calculus - Scalar projection

  1. Sep 10, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the scalar and vector projection of the vector b=(3,5,3) onto the vector a=(0,1,-5) .


    2. Relevant equations



    3. The attempt at a solution

    What ive tried is multiplying all the i's and j's and k's together and adding up everything because you get a scalar answer in the end so basically...

    3*0 + 1*5 + 3*(-5)
    = -10
    then i tried to divide by the magnitude of vector |a|

    |a|=sqrt(26)

    so i get scalar projection as -10/(sqrt(26)) as my answer
     
  2. jcsd
  3. Sep 10, 2010 #2

    Dick

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    Ok, so the scalar projection is b.a/|a|. That seems ok. What's your question?
     
  4. Sep 10, 2010 #3
    Can you please explain why we divide by the magnitude of vector "a" and if my work is correct or not please?
     
  5. Sep 11, 2010 #4

    Dick

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    The scalar projection should be |b|*cos(theta) where theta is the angle between a and b. Since the dot product is given by (a.b)=|a||b|cos(theta) the scalar projection should be (a.b)/|a|. Yes, you are doing fine so far.
     
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