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Dot Product Calculation

  1. Feb 12, 2009 #1
    1. The problem statement, all variables and given/known data


    I have a problem for Work which looks like this:

    W=[(5.0i+2.0j)]N * [(2.0i+3.0j)]m
    =5.0i+2.0i+5.0i*3.0j+2.0j*2.0i+2.0j*3.0j Nm
    =[10+0+0+6]Nm = 16

    How does that work? I don't understand?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 12, 2009 #2

    LowlyPion

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    Homework Helper

  4. Feb 12, 2009 #3

    HallsofIvy

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    Staff Emeritus
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    Another way of saying what LowlyPion said is:
    i*i= 1, j*j= 1, i*j= 0, j*i= 0 (by definition- that's how i and j are defined.)

    So 5.0i*2.0i+5.0i*3.0j+2.0j*2.0i+2.0j*3.0j= (5*2)(i*i)+ (5*3)(i*j)+ (2*2)(j*i)+ (2*3)(j*j)= 10*1+ 15*0+ 4*0+ 6*1= 10+ 0+ 0+ 6= 16.
     
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