A few questions (vectors)

[dekoyl]

Some basic questions because I wasn't paying attention in the first semester of GMA.

1.
I got which is right but I don't fully understand how I got the answer (I did it visually ) Is there a proof for this?

Also for the second part of the question, is the following proof okay? (No answers for proofs)








Sorry I don't know how to do letters with tilde so it might be a bit confusing

2.
Wouldn't the origin O be G? Then how would one do

Thanks a lot. Just some "warm up" questions

[Mao]

i'm a little confused by Q1, so give me a few minutes

but Q2, O is not G. think of O as somewhere else, I usually just draw a dot on bottom left and make it O, makes it easier.

but a hint, OG = OA + BC

CD = CO + OD = -OC + (OG + BC)

[Mao]

for Q1 a, the proof is as follows:

grab the same trapezium, rotate 180 degrees, and attach it to the right. you get a parallelogram. Specifically, (imagine it visually)

hence,

and your proof seems satisfactory =]

[/0]

Are we allowed to use other geometry in conjunction with vectors (e.g. similar triangles in this case) ?

[dekoyl]

Thanks Mao; I've got it now. =]

[Mao]

Are we allowed to use other geometry in conjunction with vectors (e.g. similar triangles in this case) ?

i think so. It's SM, so really anything 'right', so long as it is not a very obscure conjecture, should be acceptable =]

[orsel]

Are we allowed to use other geometry in conjunction with vectors (e.g. similar triangles in this case) ?

To be pedantic, if the question states 'using a vector proof' or similar (seems to happen quite often), you should avoid geometry/anything unrelated to vectors just in case.

In this instance though, since it was not specified, then yes it would be allowed.

[/0]

for Q1 a, the proof is as follows:

grab the same trapezium, flip it up-side down, and attach it to the right. you get a parallelogram. Specifically, (imagine it visually)

hence,

and your proof seems satisfactory =]

Wouldn't this already assume the answer to part b)? Isn't this circular?

[hard]

isn't vectors a little later on in the specialist course? or is this GM?

[dekoyl]

For us vectors is the first thing.

[hard]

For us vectors is the first thing.

oh weird.

[Mao]

for Q1 a, the proof is as follows:

grab the same trapezium, flip it up-side down, and attach it to the right. you get a parallelogram. Specifically, (imagine it visually)

hence,

and your proof seems satisfactory =]

Wouldn't this already assume the answer to part b)? Isn't this circular?

my bad, i meant rotate 180 degrees, which doesn't rely on anything =]