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Math Help!

Forum index > Blogs
  Ace   United States. July 11 2008 07:25. Posts 5147Profile Blog 
Hey everyone I need help with a Math concept. I'm doing a long series of calculus problems on and off and for some reason I just can't approach a problem in my head right now. Hopefully TL's math geniuses can help me


The problem is dealing with curves in 3D (multi-variable calculus). I have 2 curves both in parametric form and both are functionalized (parameters are functions). One is in terms of t and the other in terms of s. The question is how do I find the angle of intersection between these 2 curves and the point they intersect?
For sake of argument:


C1 = <t-3, t^2, 1-2t>
C2 = <s+2s^2, s, 3s-4>

I don't need the answer yet. I really just need to know how to approach the problem. To find the angle between the curves I thought about normal vector operations such as Dot Product and Cross Product but those don't get me anywhere.

Right now I'm stuck and don't know how to appoach this. Any help is appreciated.
Last edit: 2008-07-11 07:34:31


**
ItEndsInTears
Old Post

  Gene   United States. July 11 2008 07:34. Posts 2845Profile Blog 
there's an equality that states the norms of some vector equals the norm of the other times cos theta where theta is the angle between the two

its very similar to the cauchy schwartz inequality.

i forgot it already though.

if thats completely irrelevant im sorry, i really did forget a lot of multivariable calc already.
Old Post

  Daveed   United States. July 11 2008 07:36. Posts 226Profile Blog 
Well, to start, where do these curves intersect?
Old Post

  Ace   United States. July 11 2008 07:38. Posts 5147Profile Blog 
I edited the OP Daveed - I need to find that also.
Last edit: 2008-07-11 07:38:27
ItEndsInTears
Old Post

  Ace   United States. July 11 2008 07:41. Posts 5147Profile Blog 
ugh nevermind. I think I've figured it out a bit. I'm so dumb:

If you break all them up into parameters you get a good lead.
ItEndsInTears
Old Post

  Ace   United States. July 11 2008 07:47. Posts 5147Profile Blog 
x1 = -3 + t
y1 = 0 + t^2
z1 = 1 - 2t

x2 = 1 +2s
y2 = 0 + s
z2 = -4 + 3s

so C1's vector =<1,1,-2> and C2's vector = <2,1,3>.

Using Dot Product or Cross Product I can find the angle and intersection.

The #s I used are all made up so it probably wont work out neatly but I'm sure this is the right approach. Any comments?
ItEndsInTears
Old Post

  Mooga   United States. July 11 2008 07:47. Posts 462Profile Blog 
To find the point of intersection, equate the x y and z coordinates of C1 and C2 to each other. To find the angle of intersection, find the normal vectors of the plane and from there you can use trig to find the angle.
Old Post

  Gene   United States. July 11 2008 08:03. Posts 2845Profile Blog 
yeah, intersection is were x1=x2 and y1=y2 and z1=z2, and if you know all the rest i guess you dont need much help. so find values of t and s that make that happen.
Old Post

  clazziquai   July 11 2008 08:12. Posts 6685Profile Blog 
no help for the mayor!

die in hell!
#1 Sea.Really Fan / #1 Nesh Fan / Terran Forever~
Old Post

  Ace   United States. July 11 2008 09:28. Posts 5147Profile Blog 
hah mafia scum!

Thanks guys, guess I just had a mind fart for the time being (was doing problems for ~4 hours straight).
ItEndsInTears
Old Post

  ShaLLoW[baY]   Canada. July 11 2008 09:30. Posts 7844Profile Blog 
We elected a Mayor who can't do calculus? NO WONDER I'M FUCKING DEAD JEEZ
Look over there ->                                                                sAviOr for life~
Old Post

  Ace   United States. July 11 2008 10:15. Posts 5147Profile Blog 
I can do calculus, was just confused for a sec
ItEndsInTears
Old Post

 
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