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Math Help - Vector arithmetic help

  1. #1
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    Vector arithmetic help

    In the figure OE:EA=1:2, AF:FB=3:1 and OG:OB=3:1. The vector OA=a and the vector OB=b.
    Find, in terms of a, b or a and b, expressions for:

    (a) OE

    (b) OF

    (c) EF

    (d) BG

    (e) FB

    (f) FG


     OE = \frac{1}{3}a

     OF = \frac{1}{4}a + \frac{3}{4}b

     EF= -\frac{1}{12}a + \frac{3}{4}b

    I am stuck on part 'd', my book says vector BG = 2b , and I cannot seem to understand how they got this?

    I know OG:OB = 1:3, so does that not mean that  OG = \frac{3}{4}b ?

    and so to get vector BG ,  OG-OB = \frac{3}{4}b - b

    that's my thinking, but the correct answer is BG=2b can someone please show me where I am going wrong.

    thank you
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  2. #2
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    OG = OB + BG
    So
    OG/OB = 1 + BG/OB
    3/1 = 1 + BG/OB
    2 = BG/Ob
    SO BG = 2OB = 2b.
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  3. #3
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    Quote Originally Posted by sa-ri-ga-ma View Post
    OG = OB + BG
    So
    OG/OB = 1 + BG/OB
    3/1 = 1 + BG/OB
    2 = BG/Ob
    SO BG = 2OB = 2b.
    thank you, I dont understand how you formed the bold bit,could you just explain why you have divided OG/OB? And where did the one come from?
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  4. #4
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    Quote Originally Posted by Tweety View Post
    thank you, I dont understand how you formed the bold bit,could you just explain why you have divided OG/OB? And where did the one come from?
    The meaning of OG:OB =3:1 is
    OG/OB = 3/1
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  5. #5
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    Quote Originally Posted by sa-ri-ga-ma View Post
    The meaning of OG:OB =3:1 is
    OG/OB = 3/1
    Okay thanks, get it now. Also if you could explain why it is 1+BG/OB ?

    Thank you.
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  6. #6
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    OG = OB + BG

    Divide OB on both the side.
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