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

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To prove that the vector (dx/ds)i + (dy/ds)j is a unit vector along the given parametric curve, first calculate the derivatives dx/ds and dy/ds from the functions x(s) and y(s). A vector is considered a unit vector if its magnitude equals one. After finding the derivatives, compute the magnitude of the vector by using the formula √((dx/ds)² + (dy/ds)²). If the resulting magnitude equals one, the vector is confirmed as a unit vector.
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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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