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At the end of lecture 19, Professor Aroux remarks that since F and T are parallel vectors, the dot product is just the length of F. Why is that true?

MIT 18.02 Multivariable Calculus, Fall 2007
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I, believe he said that it is the length of F.
I know now. That is because T is a unit vector. Recall the equation \[dr/dt=T(ds/dt)\] the left side is velocity, ds/dt is speed or magnitude, and T is unit vector that specifies direction. Since F and T are parallel and T is unit vector (all entries equal to 1), the dot product is F itself. Hope that helps

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