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Math Help - Vectors 4

  1. #1
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    Vectors 4

    Given a and b unit vectors, determine (2a-5b) . (b+3a)
    if |a+b| =sqrt3


    all a and b in the questions have a u-hat over top of them=unit vectors

    can someone please check my work:

    |a+b|=sqrt3
    |a+b|^(0.5)=(a+b)(a+b)
    3=2+2a.b
    0.5=a.b

    (2a-5b). (b+3a)
    =-13a.b+6(a)^2-5(b)^2
    =-13(0.5)+6(1)^2-5(1)^2
    =-5.5

    is my answer correct? mostly concerned about the a.b work
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    Given a and b unit vectors, determine (2a-5b) . (b+3a) if |a+b| =sqrt3
    all a and b in the questions have a u-hat over top of them=unit vectors
    3 = \left( {a + b} \right) \cdot \left( {a + b} \right) = a \cdot a + 2a \cdot b + b \cdot b = 2 + 2a \cdot b
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  3. #3
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    that's what I did, BUT, is a.b OK or do I have to do something with cos(theta)=0.5
    I dont think I do, because I already found a.b, correct? so just plug it into the eqtn below, right?

    |a+b|=sqrt3
    |a+b|^(0.5)=(a+b)(a+b)
    3=2+2a.b
    0.5=a.b

    (2a-5b). (b+3a)
    =-13a.b+6(a)^2-5(b)^2
    =-13(0.5)+6(1)^2-5(1)^2
    =-5.5
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  4. #4
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    Yes you're right but it is:

    |a+b|^2 = (a+b).(a+b)
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  5. #5
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    sorry, that's what i meant
    the squared not the sqrt, but other than that i don't need to use any other formula right
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