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[Community Question] Linear-algebra: Vector Calculus proof part derivation.

One of our user asked:

I am following a proof in my vector calculus book but I am getting stuck.

Let T(s) be the the unit tangent vector at s. and let k(s) = norm( T’(s)) here T’(s) is orthogonal to T(s) and let N(s) be the Unit vector such that T’(s)=k(s)*N(s)

See photoenter image description here

Now, in the proof it says:

Differentiate N(s) • T(s) =0 Gives N’(s)•T(s)+N(s)•T’(s) =0

Hence N’(s)•T(s)=-k(s) But I don’t see how this Is derived?

Also , written on mobile as this is the only access I have at the moment, please go easy on the syntax.


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