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.
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?
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.