|
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.
 
|
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.
|
Well, to start, where do these curves intersect?
|
I edited the OP Daveed - I need to find that also.
|
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.
|
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?
|
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.
|
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.
|
no help for the mayor!
die in hell!
|
hah mafia scum!
Thanks guys, guess I just had a mind fart for the time being (was doing problems for ~4 hours straight).
|
We elected a Mayor who can't do calculus? NO WONDER I'M FUCKING DEAD JEEZ :p
|
I can do calculus, was just confused for a sec
|
|
|
|
|
|
WCS
