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

Finding eqn of tangent plane without eqn of surface

  • Thread starter dispiriton
  • Start date
  • #1

Homework Statement


I need to find the tangent plane of a surface S at a point P without being given the eqn of the surface. I am also given that two curves lie on this surface


Homework Equations


Point P: (2,1,3)
Curve 1: <2+3t, 1 - (t^2), 3 - 4t + (t^2)>
Curve 2: <1+ (u^2), 2(u^3) - 1, 2u+1>


The Attempt at a Solution

 

Answers and Replies

  • #2
uart
Science Advisor
2,776
9
Here's an outline.

- To find the equation of the plane you need to find the direction of the normal vector.

- Use the two given surface curves to find two vectors that lie in (are parallel to) the surface.

- Given the above two vectors it should be easy to find a vector perpendicular to both.
 
  • #3
So after I've found direction of tangent line to the two curves I cross them to find a normal vector to plane which i use to define the plane. But this final plane I define, is it the equation of the tangent plane through P already or is it only the equation of the surface?
 
  • #4
33,168
4,852
So after I've found direction of tangent line to the two curves I cross them to find a normal vector to plane which i use to define the plane. But this final plane I define, is it the equation of the tangent plane through P already or is it only the equation of the surface?
It's the equation of the tangent plane.
 
  • #5
134
0
Assuming both those curves pass through the point of interest (easily checked) then you simply want to find the tangent vector of both curves at said point. Both these vectors will lie in the tangent plane.

From there simply take the cross product of the two vectors to get the normal vector and you'll have your plane!
 

Related Threads for: Finding eqn of tangent plane without eqn of surface

Replies
17
Views
5K
Replies
5
Views
321
  • Last Post
Replies
4
Views
6K
Replies
6
Views
307
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
10
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
17
Views
2K
Top