Finding the point of intersection between two curves. (Vectors)

  • Thread starter Jaqsan
  • Start date
  • #1
17
0

Homework Statement



At what point do the curves r1(t) = (t, 4-t, 63+t^2) and r2(s)= (9-s, s-5, s^2) intersect?
Answer in the form: (x,y,z) = ____

Find the angle of intersection theta to the nearest degree.

Homework Equations





The Attempt at a Solution



i: t=9-s
j: 4-t=s-5
k: 63+t^2=s^2

i/j: t-9s
k: 63+(9-s)^2=s^2
"Solving for "s""
s=8
t=1
...
I know not what to do from here. :-(
 

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
38
Welcome to PF Jaqsan,

Homework Statement



At what point do the curves r1(t) = (t, 4-t, 63+t^2) and r2(s)= (9-s, s-5, s^2) intersect?
Answer in the form: (x,y,z) = ____

Find the angle of intersection theta to the nearest degree.

Homework Equations





The Attempt at a Solution



i: t=9-s
j: 4-t=s-5
k: 63+t^2=s^2

i/j: t-9s
k: 63+(9-s)^2=s^2
"Solving for "s""
s=8
t=1
...
I know not what to do from here. :-(

It sounds like you want to find the "direction" of each curve at the point of intersection. Can you think of a vector that describes this, and how to compute that vector given r(t)?
 
  • #3
17
0
I don't understand. The question asks for the point of intersection of the two curves. Do I find the derivative, dot product? Just point me in the right direction please.
 
  • #4
17
0
Welcome to PF Jaqsan,



It sounds like you want to find the "direction" of each curve at the point of intersection. Can you think of a vector that describes this, and how to compute that vector given r(t)?


I don't understand. The question asks for the point of intersection of the two curves. Do I find the derivative, dot product? Just point me in the right direction please.
 
  • #6
Dick
Science Advisor
Homework Helper
26,263
619
I don't understand. The question asks for the point of intersection of the two curves. Do I find the derivative, dot product? Just point me in the right direction please.

You already found the intersection point correctly. So the two tangent vectors are r1'(1) and r2'(8). What are they? Then the angle between two vectors a and b is a.b/(|a||b|). Use that.
 
  • #7
17
0
You already found the intersection point correctly. So the two tangent vectors are r1'(1) and r2'(8). What are they? Then the angle between two vectors a and b is a.b/(|a||b|). Use that.

Okay, so I got
r1'(1) = <1,-1,2>
r2'(8)= <-1,1,16>
So do I dot them to get them in one (x,y,z) form?
 
  • #8
Dick
Science Advisor
Homework Helper
26,263
619
Okay, so I got
r1' = <1,-1,2>
r2' = <-1,1,16>
So do I dot them to get them in one (x,y,z) form?

Ummm, to answer the (x,y,z)=___ you just substitute. To answer the angle question you want to form a dot product.
 
  • #9
17
0
You already found the intersection point correctly. So the two tangent vectors are r1'(1) and r2'(8). What are they? Then the angle between two vectors a and b is a.b/(|a||b|). Use that.

Ummm, to answer the (x,y,z)=___ you just substitute. To answer the angle question you want to form a dot product.

I thought I already did the substitution. r1' = <1,-1,2> r2' = <-1,1,16> What I'm trying is it looks like there are two numbers for each value <x,y,z>
 
  • #10
Dick
Science Advisor
Homework Helper
26,263
619
I thought I already did the substitution. r1' = <1,-1,2> r2' = <-1,1,16> What I'm trying is it looks like there are two numbers for each value <x,y,z>

You substituted correctly into the derivatives. That's fine. When they are asking for the intersection point (x,y,z) you should substitute t=1 into r1(t) or s=8 into r2(s). That's what you calculated for the intersection point, yes? They had better both be the same.
 
Last edited:
  • #11
17
0
You substituted correctly into the derivatives. That's fine. When they are asking for the intersection point (x,y,z) you should substitute t=1 into r1(t) or s=8 into r2(s). That's what you calculated for the intersection point, yes? They had better both be the same.

Thanks. I figured it out. I was just being retarded. My answers are (1,3,64) and 40degrees
 
Last edited:
  • #12
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
38
Thanks. I figured it out. I was just being retarded. My answers are (1,3,36) and 40degrees

I think you mean (1,3,64), right?
 
  • #13
17
0
I think you mean (1,3,64), right?

My bad. Exhibiting my retardness once again. (1,3,64) and 40 degrees.
 

Related Threads on Finding the point of intersection between two curves. (Vectors)

Replies
17
Views
38K
Replies
4
Views
51K
Replies
7
Views
2K
Replies
0
Views
18K
  • Last Post
Replies
13
Views
2K
Replies
5
Views
1K
  • Last Post
Replies
11
Views
3K
Replies
1
Views
3K
Replies
14
Views
29K
Replies
0
Views
2K
Top