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Math Help - Vectors and Hexagon

  1. #1
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    Vectors and Hexagon

    I've been at this question for a few hours and I'm stuck. I really need to see someone show the work so I can finally understand and "get it".

    In Figure (see attached picture), A, B, C, D, E, and F, are the vertices of a regular hexagon centered at the origin.

    Express each of the following vectors in terms of a = vec(OA) and b = vec(OB):

    a) vec(AB)
    b) vec(BC)
    c) vec(AD)
    d) vec(CF)
    e) vec(AC)
    f) vec(BC) + vec(DE) + vec(FA)

    I've tried for hours. I think a) I get vec(AB) = b - a
    but on question b I also get b - a even though I know it should probably be -a
    The rest I'm messed up on bad. But on question f) I think it should be = 0.

    Can someone show me the work? I am so lost and yet this seems so easy. I just need to see how to do it properly so I can finally get it. This isn't for marks btw, it's just to learn.
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  2. #2
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    Quote Originally Posted by Ulchie View Post
    I've been at this question for a few hours and I'm stuck. I really need to see someone show the work so I can finally understand and "get it".

    In Figure (see attached picture), A, B, C, D, E, and F, are the vertices of a regular hexagon centered at the origin.

    Express each of the following vectors in terms of a = vec(OA) and b = vec(OB):

    a) vec(AB)
    b) vec(BC)
    c) vec(AD)
    d) vec(CF)
    e) vec(AC)
    f) vec(BC) + vec(DE) + vec(FA)

    I've tried for hours. I think a) I get vec(AB) = b - a
    but on question b I also get b - a even though I know it should probably be -a
    The rest I'm messed up on bad. But on question f) I think it should be = 0.

    Can someone show me the work? I am so lost and yet this seems so easy. I just need to see how to do it properly so I can finally get it. This isn't for marks btw, it's just to learn.
    Since you have a regular hexagon, the angles are all the same.

    Vector AB = OA - OB.

    Now, if you multiple vector AB by the positive angle, you will get BC. Get the idea?
    Last edited by dwsmith; January 29th 2011 at 09:24 PM.
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  3. #3
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    Quote Originally Posted by Ulchie View Post
    I've been at this question for a few hours and I'm stuck. I really need to see someone show the work so I can finally understand and "get it".

    In Figure (see attached picture), A, B, C, D, E, and F, are the vertices of a regular hexagon centered at the origin.

    Express each of the following vectors in terms of a = vec(OA) and b = vec(OB):

    a) vec(AB)
    b) vec(BC)
    c) vec(AD)
    d) vec(CF)
    e) vec(AC)
    f) vec(BC) + vec(DE) + vec(FA)

    I've tried for hours. I think a) I get vec(AB) = b - a
    but on question b I also get b - a even though I know it should probably be -a
    The rest I'm messed up on bad. But on question f) I think it should be = 0.

    Can someone show me the work? I am so lost and yet this seems so easy. I just need to see how to do it properly so I can finally get it. This isn't for marks btw, it's just to learn.
    1. \overrightarrow{OC} = \overrightarrow{AB}=b-a

    2. \overrightarrow{BC}=\overrightarrow{OC}-b=(b-a)-b
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  4. #4
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    I thought VEC AB = OB - OA ??

    a + (b - a) = b
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  5. #5
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    Thanks for the reply!

    Okay, so out of curiosity how would you show your work for #1?
    vec(AB)= vec(OA) + vec(OB) - vec(OA)
    then what? how do you know to get rid of the first vec(OA) and not the second one with the vec(OB)? I almost feel like just adding them but ie: a+b-a=b but to know to keep the b-a...?

    I find it gets complicated with c, d, e, f. In f I'm pretty sure it should be vec(0).

    I know it's a pain but could you show another step or two?
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  6. #6
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    Quote Originally Posted by Ulchie View Post
    Thanks for the reply!

    Okay, so out of curiosity how would you show your work for #1?
    vec(AB)= vec(OA) + vec(OB) - vec(OA)
    then what? how do you know to get rid of the first vec(OA) and not the second one with the vec(OB)? I almost feel like just adding them but ie: a+b-a=b but to know to keep the b-a...?

    I understand number 2, except algebraically i feel like i want to cancel the b's. But I don't want to find the displacement so I guess that's why we don't...?

    I find it gets complicated with c, d, e, f. In f I'm pretty sure it should be vec(0).

    I know it's a pain but could you show another step or two?
    You are correct AB = OB - OA
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  7. #7
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    I just noticed that if you draw your regular hexagon in the unit circle, you should be able to solve it pretty quickly.
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  8. #8
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    Okay I'm so close to understanding this it hurts.

    a + b - a = b I get that algebraically. However, how do you know to only keep the (b-a) for the answer?

    same goes for part b)

    b + c - b = c where c=b-a
    b + (b-a) - b = c why do we keep (b-a)-b as the answer? what happened to the first b? or the other side of the equation.

    I'm missing some rule or something... cause I don't understand. That's where I'm messing up I think.
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