Curve of intersection of surfaces

In summary, the conversation discusses a problem involving two curves and finding their intersection in the first octant. The person asking the question has been able to sketch the curves individually but is struggling to visualize how they intersect. They ask if finding parametric equations for x, y, and z would help and if looking at values of t for which x=0, y=0, and z=0 would indicate the endpoints of the curve. They are seeking suggestions or tips for solving the problem.
  • #1
jegues
1,097
3

Homework Statement



See first figure attached

Homework Equations





The Attempt at a Solution



I was able to sketch the two curves individually to get an idea of what I'm looking at, but I still can't really visualize how the two curves would intersect each other in the first octant.

Is this crucial to answering this question?

If I can write parametric equations for x, y and z then I could express the curve of intersection in that form. Then I'd simply have to look at values of t for which x=0, y=0 and z=0, right? Those would be the endpoints of the curve when they are exiting the first octant.

Any ideas/suggestions/tips?

Thanks again!
 

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  • #2
Bump, still looking for some help on this one!
 

1. What is the curve of intersection of surfaces?

The curve of intersection of surfaces is the set of points where two or more surfaces intersect and share a common boundary. It can be a line, a circle, an ellipse, etc., depending on the shapes and orientations of the intersecting surfaces.

2. How is the curve of intersection of surfaces calculated?

The curve of intersection of surfaces can be calculated by solving the equations of the intersecting surfaces simultaneously. This can be done algebraically or graphically, depending on the complexity of the surfaces.

3. What information can be obtained from the curve of intersection of surfaces?

The curve of intersection of surfaces can provide information about the points where the surfaces intersect, such as the coordinates and the type of intersection (tangent, intersecting, etc.). It can also give insights into the shapes and orientations of the surfaces.

4. Can the curve of intersection of surfaces be used in real-world applications?

Yes, the curve of intersection of surfaces has various applications in fields such as engineering, physics, and computer graphics. It can be used to model and analyze the interactions between different surfaces, which is essential in designing structures, simulating physical phenomena, and creating 3D models.

5. Are there any limitations to the curve of intersection of surfaces?

One limitation of the curve of intersection of surfaces is that it is only applicable to two or more intersecting surfaces. It cannot be used for surfaces that do not intersect or intersect at a single point. Additionally, the calculations can become increasingly complex as the number of surfaces increases.

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