How Do You Prove a Vector is Unit Along a Parametric Curve?

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SUMMARY

The discussion focuses on proving that the vector defined by the derivatives of the parametric equations x(s) = rcos(s/r) and y(s) = rsin(s/r) is a unit vector along the curve defined by the function f(x,y) = xy + x + y. Participants emphasize the importance of calculating the derivatives dy/ds and dx/ds to establish the unit vector condition. The key steps involve differentiating the parametric equations and then normalizing the resulting vector.

PREREQUISITES
  • Understanding of parametric equations and their derivatives
  • Knowledge of vector calculus, specifically unit vectors
  • Familiarity with trigonometric functions and their derivatives
  • Basic comprehension of the concept of normalization in vector mathematics
NEXT STEPS
  • Calculate the derivatives dy/ds and dx/ds for the given parametric equations
  • Learn about the normalization process for vectors
  • Study the properties of unit vectors in vector calculus
  • Explore applications of parametric curves in physics and engineering
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Students and professionals in mathematics, physics, and engineering who are working with parametric curves and vector analysis, particularly those interested in understanding unit vectors and their applications.

brunette15
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Hey everyone,

I am given the following function f(x,y) = xy+x+y along the curve x(s)=rcos(s/r) and y(s)=rsin(s/r). I have to show that (dx/s)i + (dy/ds)j is a unit vector.

I am unsure where to begin with this :/

Can anyone please give me some hints/ideas on how to approach this question?
 
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Hi brunette15,

What does it mean when a vector is a unit vector? Let's start by finding $\d{y}{s}$ and $\d{x}{s}$.
 

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