addition and subtraction of vectors

[dcc]

have you ever heard of the parallelogram law of addition? or even adding vectors head to tail?



see? they added vectors! despite the fact that position vectors are bound, you can still add them.

if your still not convinced, try:
http://www.physicsforums.com/showpost.php?p=827759&postcount=27

[Collin Li]

dcc, you are missing the point. A position vector is a vector that begins from the origin. They are not "free," which means you cannot just take the vector b and move it to the head of a, because it is fixed to the origin.

That is evaporade's point.

[evaporade]

initial position + displacement = final position.
what is initial position + final position ?

parallelogram law is a convenient way of adding two vectors (not position vectors), it is a direct consequence of putting vectors head to tail in addition.

[evaporade]

i am glad someone agrees

[Mao]

i am glad someone agrees

erm, coblin outlined your point, it didnt say he agrees with you.

that aside:
i see absolutely no point of this debate (much like the one in methods)
it is irrelevant to the respective subjects these threads are in, and unless you are an absolute purist, I see little point in exploring this issue. The practicality of this debate is minimal (if there are any at all). I can just as easily say a position vector is a displacement vector from O, which makes absolutely no difference on its magnitude nor direction.

I do give credit that position vectors does differentiate from displacement vectors. (e.g. John's house is 3km west of me, and Joe's house is 4km north of me, but the sum of these two position vectors bears absolutely no meaning)
While that is open for interpretations, the sum can be given meanings. such as the square vertices example.

and that aside as well, I DO have a problem with the way this problem was presented.
It just happens that evaporade = enpassant, and clearly the questions were asked with agendas in mind. If you would like to present a challenge, please do, we have high respects for those who proposes challenges, http://vcenotes.com/forum/index.php/topic,11.0.html is an example.
there is NO point (in fact i find it offensive) to present these "challenges" in the format of a question, then using this opportunity to refute the suggested solutions, especially when they were done in mind of the VCE syllabus. whatever you are trying to achieve, you have earnt a place in my "troll" list.

please dont let this happen again

specifically, there are rules set up against exactly what you are doing (i suggest you look it up). I am hoping it doesnt piss me off to the point where i see fit to do something about it.

oh, and, there is a "modify" button. please avoid double-posting (or triple)

[Collin Li]

I agree with evaporade, but I also agree that such rigorous definition of vectors does not take place in VCE Specialist Maths.

[enpassant]

Have you ever thought of two users of the same computer.

Quote 'clearly the questions were asked with agendas in mind........... we have high respects for those who proposes challenges,'  Contradictory.

Quote 'I DO have a problem with the way this problem was presented.' Clearly you have a problem.

I disagree with coblin. It was not a rigorous discussion by evaporade. It merely pointed out the misconception about position and displacement vectors, which is so common as shown in this forum.

[Collin Li]

I said the definition is rigorous.

I understand your point: it is that the term 'position vector' seems to be misused. However, the point is trivial, as when addition of vectors is required, we simply unhook the position vector from the origin, making it a free vector. The VCE syllabus is not concerned with this technicality. I understand everyone else's frustration, but I value your point.

[evaporade]

In the current study design under Vectors:
Quote 'Vectors, including addition and subtraction of vectors and ......, position vectors;'

So, coblin, you are 100% sure the VCE syllabus is not concerned with this technicality (difference between position and displacement vectors), and it is right to say adding two position vectors to obtain a third position vector.

'I understand everyone else's frustration' I don't think everyone was frustrated, only those who thought and insisted on position and displacement vectors are the same were frustrated. Students with an open mind would find this a valuable information.

[evaporade]

Let me add a bit more before I ....

Very often you see in textbooks, let vector OA = a and vector OB = b. This is to replace position vectors with free vectors so that addition can be carried out.

[Mao]

'I understand everyone else's frustration' I don't think everyone was frustrated, only those who thought and insisted on position and displacement vectors are the same were frustrated. Students with an open mind would find this a valuable information.

valuable such that it can be argued over and over?

i see absolutely no purpose making this distinction, especially not in this course.
the position vector you quoted from the study design refers to an understanding of what position vectors are: displacement vectors with reference to the point of origin.

this discussion is synonymous with the argument in philosophy that you can never cross the same river twice. sure, the water flows  and it can never be the same river. so what? what is the point?

are we now going forth to argue that 2-3=-1 is a misconception? because it really should be 2+(-3)=-1?

oh, and

(Image removed from quote.)

it exists for a reason

[evaporade]

only those who thought and insisted on position and displacement vectors are the same were frustrated. Students with an open mind would find this a valuable information.

It takes more than one to argue.

coblin values my point.

you can stop the argument by stopping arguing and denigrating

[Mao]

okay let me sum up what is happening here:

enpassant asks a question, evaporade refuted the reply, saying

Subtraction of two position vectors gives displacement (change in position), but addition of two position vectors is undefined.

the distinction between position and free vectors are then made, acknowledged by both coblin and myself

I do give credit that position vectors does differentiate from displacement vectors. (e.g. John's house is 3km west of me, and Joe's house is 4km north of me, but the sum of these two position vectors bears absolutely no meaning)
While that is open for interpretations, the sum can be given meanings. such as the square vertices example.

...I value your point.

dcc, however, disagreed, and exited the argument

since the beginning, however, I have expressed the lack of practicality of this definition, and coblin later joined me:

The first two are displacement vectors, not position vectors. I think you are confused with position and displacement vectors.

i'm sorry, the use for being this pedantic is?

i see absolutely no point of this debate (much like the one in methods)
it is irrelevant to the respective subjects these threads are in, and unless you are an absolute purist, I see little point in exploring this issue. The practicality of this debate is minimal (if there are any at all). I can just as easily say a position vector is a displacement vector from O, which makes absolutely no difference on its magnitude nor direction.

I agree with evaporade, but I also agree that such rigorous definition of vectors does not take place in VCE Specialist Maths.

...However, the point is trivial, as when addition of vectors is required, we simply unhook the position vector from the origin, making it a free vector. The VCE syllabus is not concerned with this technicality.

i see absolutely no purpose making this distinction, especially not in this course.
the position vector you quoted from the study design refers to an understanding of what position vectors are: displacement vectors with reference to the point of origin.

yet it continues...

anyone else sees the irony when evaporade asks to

you can stop the argument by stopping arguing and denigrating

[enwiabe]

Evaporade: I have placed your IP making numerous posts from the same accounts.

The 'two user' computer argument fails simply because anyone with a rational mind can see that this is completely contrived, and, your writing style does not differ from 'enpassant' to 'evaporade'. Epic fail. I'm not going to ban you because all you have done is be an annoying little shit. I don't think your little mental toss-off *really* counts as the kind of trolling that should be banned. But seriously, you look really pathetic. To everyone.

[AppleXY]

evaporade and enpassant sound similar. I don't know, it just does.