3. Let C be an oriented curve parameterized by r(t), where a ≤t≤ b. Suppose that the following two items are also true: (i) ♬ is always tangent to C in the direction of orientation, and (ii) ||F|| is constant, say ||F|| = m, everywhere along C (see diagram below). (a) What is the angle between F and dr? (b) Use the geometric definition of the dot product to explain why F. dr must equal ||F||||dr||. (c) Use the above information to explain why √ F - d² = m. dr (Length of C). dr

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