1. ## 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)
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.

2. Originally Posted by Ulchie
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)
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?

3. Originally Posted by Ulchie
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)
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. $\overrightarrow{BC}=\overrightarrow{OC}-b=(b-a)-b$

4. I thought VEC AB = OB - OA ??

a + (b - a) = b

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?

6. Originally Posted by Ulchie

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

7. I just noticed that if you draw your regular hexagon in the unit circle, you should be able to solve it pretty quickly.

8. 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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# hexagon vector quetions

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