IHopetoImprove
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I can't really start reading up on this question as I don't know what topic it is. Can anyone help?

True or false: if u is perpendicular to v and w thenuis perpendicular tov+ 2w.Give a proof if true, or a counterexample if false
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mqb2766
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(Original post by IHopetoImprove)
I can't really start reading up on this question as I don't know what topic it is. Can anyone help?

True or false: if u is perpendicular to v and w thenuis perpendicular tov+ 2w.Give a proof if true, or a counterexample if false
Geometry, linear algebra, ... It should be straightforward using the appropriate defn of perpendicular.
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RDKGames
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(Original post by IHopetoImprove)
I can't really start reading up on this question as I don't know what topic it is. Can anyone help?

True or false: if u is perpendicular to v and w thenuis perpendicular tov+ 2w.Give a proof if true, or a counterexample if false
Consider \mathbf{u} \cdot (\mathbf{v} + 2\mathbf{w})
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IHopetoImprove
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(Original post by RDKGames)
Consider \mathbf{u} \cdot (\mathbf{v} + 2\mathbf{w})
I mean I'm thinking vectors but that's a pretty big domain. And I'm not really sure what multiplying them would do? I don't really understand why u being perpendicular would mean you multipy. Nor can I visualise it being perpendicular to two things either, I really just need to know some background.
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mqb2766
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(Original post by IHopetoImprove)
I mean I'm thinking vectors but that's a pretty big domain. And I'm not really sure what multiplying them would do? I don't really understand why u being perpendicular would mean you multipy. Nor can I visualise it being perpendicular to two things either, I really just need to know some background.
How do you show two vectors are perpendicular?
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IHopetoImprove
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Yes, or rather, what does this mean practically?
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RDKGames
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(Original post by IHopetoImprove)
Yes, or rather, what does this mean practically?
Two vectors are perpendicular if they intersect each other at 90 degree angles. This is elementary geometry.

I would expect you know this if you are attempting this question?

With more theory, you would see that two vectors are perpendicular if their dot product is zero.
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mqb2766
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(Original post by IHopetoImprove)
Yes, or rather, what does this mean practically?
A quick Google tells you the definition.
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ghostwalker
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:holmes:

I'd look for a counter-example. The dot product being zero has a caveat.
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IHopetoImprove
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OK, that is more what I'm asking, their dot product is zero is useful info I can work from, thank you.
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IHopetoImprove
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OK, that is more what I'm asking, their dot product is zero is useful info I can work from, thank you.

(Original post by ghostwalker)
:holmes:

I'd look for a counter-example. The dot product being zero has a caveat.
Thank you.
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davros
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(Original post by IHopetoImprove)
I mean I'm thinking vectors but that's a pretty big domain. And I'm not really sure what multiplying them would do? I don't really understand why u being perpendicular would mean you multipy. Nor can I visualise it being perpendicular to two things either, I really just need to know some background.
Surely if you're being asked this question as part of a uni course then you've been given a context for it, i.e. you know what module you're studying and what objects you're working with? I mean are you doing a Geometry course where vectors can be used to represent real physical entities like lines or sides of a shape and you can see what "perpendicular" means, or are you doing a more abstract linear algebra course where you're given a purely abstract definition of perpendicularity for two objects??
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(Original post by davros)
Surely if you're being asked this question as part of a uni course then you've been given a context for it, i.e. you know what module you're studying and what objects you're working with?
You know, I'm getting very concerned about the way Universities seem to be teaching mathematics these days. Apparently it's now the norm to set questions in areas that aren't covered in the course - indeed, speaking to the students it seems likely no mathematics at all has actually been covered since term started. What's more, there seem to be severe bandwidth limits on uploads, preventing the poor students from ever being able to upload anything even remotely resembling an attempt at answering a question.
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davros
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(Original post by DFranklin)
You know, I'm getting very concerned about the way Universities seem to be teaching mathematics these days. Apparently it's now the norm to set questions in areas that aren't covered in the course - indeed, speaking to the students it seems likely no mathematics at all has actually been covered since term started. What's more, there seem to be severe bandwidth limits on uploads, preventing the poor students from ever being able to upload anything even remotely resembling an attempt at answering a question.
That sounds pretty unbelievable - almost as if they want students to drop out after Xmas!!

I have a lot of sympathy for new students not knowing how to structure a proof initially, or even knowing which parts of a complex definition can be lifted out to use in a proof, but if they aren't even given a clue as to their topic of investigation then things are really looking pretty bleak for them.
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IHopetoImprove
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(Original post by ghostwalker)
:holmes:

I'd look for a counter-example. The dot product being zero has a caveat.
Right, may I show you my interpretation of that so you may see where I am completely misundestanding.

counter e.g. >> v = i + j , w = 2i + 2j

v * w = i * 2i + j * 2j = 2i + 2j ??? (not sure if this is correct at all)

v + 2w = (i + j) + (2i + 2j) = 3i + 3j != v*w

I don't see where perpendicularness comes into it?
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IHopetoImprove
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(Original post by davros)
Surely if you're being asked this question as part of a uni course then you've been given a context for it, i.e. you know what module you're studying and what objects you're working with? I mean are you doing a Geometry course where vectors can be used to represent real physical entities like lines or sides of a shape and you can see what "perpendicular" means, or are you doing a more abstract linear algebra course where you're given a purely abstract definition of perpendicularity for two objects??
I mean yes but I have probably with online teaching and everything missed where perpendicularness comes into things, I see you misunderstand me so let me show you what I mean.

I am 90% sure this is the wrong direction.

counter e.g. >> v = i + j , w = 2i + 2j


v * w = i * 2i + j * 2j = 2i + 2j ??? (not sure if this is correct at all)


v + 2w = (i + j) + (2i + 2j) = 3i + 3j != v*w


I don't see where perpendicularness comes into it?
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davros
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(Original post by IHopetoImprove)
I mean yes but I have probably with online teaching and everything missed where perpendicularness comes into things, I see you misunderstand me so let me show you what I mean.

I am 90% sure this is the wrong direction.

counter e.g. >> v = i + j , w = 2i + 2j


v * w = i * 2i + j * 2j = 2i + 2j ??? (not sure if this is correct at all)


v + 2w = (i + j) + (2i + 2j) = 3i + 3j != v*w


I don't see where perpendicularness comes into it?
Well, as we suggested above, you absolutely need a definition of what "perpendicular" means for your vectors. And also you are supposed to be working with 3 vectors u, v and w, not just v and w, so what you've written above isn't a "proof" (or counterexample) for your original statement.
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(Original post by IHopetoImprove)
I mean yes but I have probably with online teaching and everything missed where perpendicularness comes into things, I see you misunderstand me so let me show you what I mean.
Which subject are you studying and where? Did you do A-level Maths?
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IHopetoImprove
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(Original post by davros)
Well, as we suggested above, you absolutely need a definition of what "perpendicular" means for your vectors. And also you are supposed to be working with 3 vectors u, v and w, not just v and w, so what you've written above isn't a "proof" (or counterexample) for your original statement.
OK, I don't understand what you're trying to say "what perpendicular means" can mean either 1) -> definition -> if these two lines were extended out indefinately they must meet at right angles or 2) > it *means* that due to some property of vectors you have gained some extra infomation which will allow you to solve the problem.

So my issue in the question is 2) that I have 0 bloody idea how perpendicularity plays into the problem hence I have no idea what u really does in the context of the question.
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IHopetoImprove
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(Original post by DFranklin)
Which subject are you studying and where? Did you do A-level Maths?
I did a level maths be it a while ago but I don't remember perpendicularity of 1) vectors giving more infomation in order to determine something about the vectors it is perpendicular to and 2) I cant think of any solution myself 3) nor do I know where to look to find infomation I need in order to work it out.
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