• Support PF! Buy your school textbooks, materials and every day products Here!

Horizontal Tangent Lines: Intersection of Cylinder and Plane

  • Thread starter Lothar
  • Start date
  • #1
19
0

Homework Statement



Consider the plane z = x + 2y and the cylinder x^2 + y^2 = 1

(a) Find a vector function r(t) describing their intersection.
(b) Find the points if any where the tangent to ~r is horizontal
(c) Find an equation for the tangent line to ~r at each of these points.


Homework Equations




The Attempt at a Solution



r(t) = cos(t)i+sin(t)j+(cos(t)+2sin(t))k
r'(t) = -sin(t)i + cos(t)j + (-sin(t)+2cos(t))k

These equations are correct, as I have plotted them in Maple 14 and the images appear correct. I'm having issues finding the horizontal tangent, and then finding the equations afterwards.
The horizontal tangent should be when r'(t) = 0 correct? I cannot find a value that makes this true. Maybe I'm making a mistake in my thinking?

Thank you for any help.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
250
Hi Lothar! :smile:

(try using the X2 icon just above the Reply box :wink:)
The horizontal tangent should be when r'(t) = 0 correct?
No.

r' is a vector, it will be horizontal when … ? :wink:

(if r' was zero somewhere, you'd have a dodgy parameter! :rolleyes:)
 
  • #3
19
0
Hi Lothar! :smile:

(try using the X2 icon just above the Reply box :wink:)


No.

r' is a vector, it will be horizontal when … ? :wink:

(if r' was zero somewhere, you'd have a dodgy parameter! :rolleyes:)
Where r' is equal to pi or 2pi? Maybe? I'm kind of lost now.
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
250
Are we talking about the same thing? :confused:

r' is a vector, of the form (a,b,c) or ai + bj + ck

it can't be a number like π ror 2π …

when will that vector be horizontal?​
 
  • #5
19
0
Are we talking about the same thing? :confused:

r' is a vector, of the form (a,b,c) or ai + bj + ck

it can't be a number like π ror 2π …

when will that vector be horizontal?​
I'm not sure. That's why I asked.
When the j component is equal to zero?
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,832
250
When the j component is equal to zero?
Nearly :rolleyes: … the k component! :wink:

(isn't that obvious … "horizontal" means moving only in the x,y plane, so no z ?)
 
  • #7
19
0
Well I'm stupid. Still though, I don't see a point on the unit circle where 2cost - sint is equal to zero.
 
  • #8
tiny-tim
Science Advisor
Homework Helper
25,832
250
tant = 2 :smile:
 

Related Threads on Horizontal Tangent Lines: Intersection of Cylinder and Plane

  • Last Post
Replies
1
Views
57K
  • Last Post
Replies
2
Views
7K
Replies
8
Views
2K
Replies
1
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
7K
  • Last Post
Replies
1
Views
2K
  • Last Post
2
Replies
25
Views
7K
  • Last Post
Replies
5
Views
7K
Replies
5
Views
2K
Top