Decomposing a Vector into Parts

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Feb 10, 2022.

  1. nycmathguy

    nycmathguy

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    Section 6.4

    Can you please do 58 as a guide for me to do the rest?


    Screenshot_20220206-121827_Samsung Notes.jpg
     
    nycmathguy, Feb 10, 2022
    #1
  2. nycmathguy

    MathLover1

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    58.

    given:

    u=<0,3>
    v=<2,15>

    1: first find projection of u =<0,3>onto v =<2,15>

    (u.v)/|v|*v/|v|

    =(u*v)/(|v|)^2*v

    u*v=0*2+3*15=45

    (|v|)^2=(sqrt(2^2+15^2)^2=229

    =45/229*<2,15>

    =<2(45/229),15(45/229)>

    =<90/229,675/229>

    2: Find the orthogonal component

    w2 = u - w1
    w2 = <0,3> - <90/229,675/229>
    w2 = <0-90/229,3-675/229>
    w2 = <-90/229, 12/229>

    3: Write the vector as the sum of two orthogonal vectors.

    u = w1 + w2
    u = <90/229,675/229> + <-90/229, 12/229>
    u = <90/229-90/229, 675/229+12/229>
    u =<0, 3>
     
    MathLover1, Feb 11, 2022
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  3. nycmathguy

    nycmathguy

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    What do you mean by w2 and w1?
     
    nycmathguy, Feb 11, 2022
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  4. nycmathguy

    MathLover1

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    the orthogonal components
     
    Last edited: Feb 11, 2022
    MathLover1, Feb 11, 2022
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  5. nycmathguy

    nycmathguy

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    Thank you. I have my work cut out for me this weekend. Is this not a cool idea? You help me by answering questions.

    I then use your step by step reply to answer similar textbook problems and only return here if needed. However, since I know you love mathematics and, just like me can't get enough numbers, I will keep you busy by posting David Cohen questions on the side. We both like David Cohen, right?
     
    nycmathguy, Feb 11, 2022
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  6. nycmathguy

    nycmathguy

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    IMG_20220212_190257.jpg

    IMG_20220212_190306.jpg

    IMG_20220212_190318.jpg
     
    nycmathguy, Feb 13, 2022
    #6
  7. nycmathguy

    MathLover1

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    correction:
    u=<-56/17+5/17,-14/17-20/17>=<-3,-2>
     
    MathLover1, Feb 13, 2022
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  8. nycmathguy

    nycmathguy

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    Ok. A basic math error that can happen to any of us.
     
    nycmathguy, Feb 13, 2022
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