= M, Let C be an oriented curve parameterized by r(t), where a t ...
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= M, Let C be an oriented curve parameterized by r(t), where a ≤ t ≤ b. Suppose that the following two items are also true: (i) F is always tangent to C in the direction of orientation, and (ii) ||F|| is constant, say ||F|| 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. dr = m drm (Length of C). dr = M, Let C be an oriented curve parameterized by r(t), where a ≤ t ≤ b. Suppose that the following two items are also true: (i) F is always tangent to C in the direction of orientation, and (ii) ||F|| is constant, say ||F|| 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. dr = m drm (Length of C). dr
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Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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