Velocity of a bee moving along the curve of intersection of 2 surfaces

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SUMMARY

The discussion centers on determining the correct function representation for the velocity of a bee moving along the curve of intersection of two surfaces. The user initially struggled to decide between the functions f2(x,y,z) = x² - y² - z and f2(x,y,z) = z - x² + y². The key insight is that the problem statement specifies the bee is moving in the increasing direction of z, which directly influences the choice of function. Ultimately, the user resolved their confusion independently.

PREREQUISITES
  • Understanding of multivariable calculus concepts, particularly surface intersections.
  • Familiarity with vector functions and their applications in motion analysis.
  • Knowledge of partial derivatives and their role in determining directional movement.
  • Basic comprehension of the geometric interpretation of functions in three-dimensional space.
NEXT STEPS
  • Study the principles of surface intersections in multivariable calculus.
  • Learn about vector fields and their applications in physics, particularly in motion analysis.
  • Explore the concept of directional derivatives and their significance in determining movement along surfaces.
  • Investigate examples of similar problems involving curves of intersection and their applications in real-world scenarios.
USEFUL FOR

Students and professionals in mathematics, physics, and engineering fields who are interested in the dynamics of motion along surfaces, particularly those studying multivariable calculus and vector analysis.

karokr94
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Hi, I've attached the problem and the solution. I understand the solution except for one thing. I've circled the part I'm having problems with. How do I decide if the circled part should be
f2(x,y,z)=x2-y2-z or
f2(x,y,z)=z-x2+y2

I'm sure it has something to do with the fact that the problem statement states that the bee is moving in the increasing direction of z, but I just can't figure out how it translates into f2 being one or the other. Or are both answers acceptable?

Thanks in advance for the help!
 

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Never mind, I figured it out.
 

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