Curve of intersection of surfaces

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SUMMARY

The discussion focuses on finding the curve of intersection between two surfaces in the first octant. The user is attempting to visualize the intersection and considers writing parametric equations for x, y, and z to express the curve. The key approach involves determining the values of the parameter t for which x=0, y=0, and z=0, which would indicate the endpoints of the curve as it exits the first octant.

PREREQUISITES
  • Understanding of parametric equations in three-dimensional space
  • Familiarity with the concept of curves of intersection between surfaces
  • Knowledge of the first octant in Cartesian coordinates
  • Basic skills in sketching and visualizing geometric shapes
NEXT STEPS
  • Research how to derive parametric equations for curves of intersection
  • Study the visualization techniques for three-dimensional surfaces
  • Learn about the implications of the first octant in multi-variable calculus
  • Explore examples of intersection curves in calculus textbooks or online resources
USEFUL FOR

Students studying multivariable calculus, mathematicians interested in geometric intersections, and educators looking for teaching resources on parametric equations and surface intersections.

jegues
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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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Bump, still looking for some help on this one!
 

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