Quick Vectors question...?(C4) Watch

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fabz
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#1
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What does it mean when 2 lines are "skew"? And how can you tell if they are?

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J.F.N
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(Original post by fabz)
What does it mean when 2 lines are "skew"? And how can you tell if they are?

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Two skew lines are lines that do not intersect and are not parallel. If you want to show that two lines are skew, it suffices to show that both these conditions do not hold.
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RichE
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(Original post by J.F.N)
That they are neither orthogonal nor parallel. You can use the dot-product to verify both--first (let the angle between them X), show that CosX is non-zero (hence the lines are not orthogonal), and then show that CosX is neither 1 nor -1 (hence the lines are not parallel).
Skew simply means that they do not meet - so the might still be parallel or orthogonal

You simply need to check that they have no solutions/points in common
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fabz
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I may be stupid but what on earth is orthogonal??? Is it like perpendicular? :confused:
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fabz
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(Original post by RichE)
Skew simply means that they do not meet - so the might still be parallel or orthogonal

You simply need to check that they have no solutions/points in common
Ahh... That makes more sense!! Cheers muchly!!
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RichE
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(Original post by fabz)
I may be stupid but what on earth is orthogonal??? Is it like perpendicular? :confused:
yes vectors are orthogonal is saying the same as them being perpendicular - but I don't agree with JFN post on this matter relating to "skew"
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J.F.N
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(Original post by RichE)
Skew simply means that they do not meet - so the might still be parallel or orthogonal

You simply need to check that they have no solutions/points in common
My impression was that skew lines are classified differently from parallel lines.
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RichE
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(Original post by J.F.N)
Yep, yep. I corrected myself.
And yes, thinking about it, skew would probably preclude their being parallel
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J.F.N
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(Original post by RichE)
And yes, thinking about it, skew would probably preclude their being parallel
Ah, good. I keep editing myself!
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fabz
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So they have to be parallel in one plane but not intersecting... or do I have the wrong end of the kebab?
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RichE
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JFN - Did the Brouwer FPT post make sense - where have you met this if you haven't yet met any topology
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J.F.N
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(Original post by RichE)
JFN - Did the Brouwer FPT post make sense - where have you met this if you haven't yet met any topology
I have met topology, but only in the Euclidean sense--that's where I encountered the trivial example of the Brouwer FPT, i.e. the IVT. I wondered how it generalized, and that's how I came across it.
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J.F.N
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(Original post by fabz)
So they have to be parallel in one plane but not intersecting... or do I have the wrong end of the kebab?
They are neither intersecting nor parallel.
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RichE
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(Original post by fabz)
So they have to be parallel in one plane but not intersecting... or do I have the wrong end of the kebab?
To be skew they have to not intersect and also not be parallel

<Some definitions of skew might include the possibility of being parallel - but unsurprisingly in practice such lines are normally simply refered to as parallel>
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fabz
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Thanks guys!
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RichE
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(Original post by J.F.N)
I have met topology, but only in the Euclidean sense--that's where I encountered the trivial example of the Brouwer FPT, i.e. the IVT. I wondered how it generalized, and that's how I came across it.
Personally think topology is one of the neatest areas of maths, but it can be quite abstract first time around
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J.F.N
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(Original post by fabz)
Thanks guys!
Oh, and moreover, any two skew lines lie in parallel planes.
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J.F.N
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(Original post by RichE)
Personally think topology is one of the neatest areas of maths, but it can be quite abstract first time around
I'm more into algebra--but the material gets to a point where excluding one or the other is impossible.
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RichE
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#19
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(Original post by J.F.N)
Oh, and moreover, any two skew lines lie in parallel planes.
True but in 3D I think parallel is usually taken to mean having the same direction and probably such lines aren't called skew (in practice at least)
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RichE
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(Original post by J.F.N)
I'm more into algebra
It's a dirty job but somebody has to do it :rolleyes:
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