Zero curvature Prove that the curve
where a, b, c, d, e, and f are real numbers and p is a positive integer, has zero curvature. Give an explanation.
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Calculus: Early Transcendentals (3rd Edition)
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- Prove that the curve r(t) = (a + bt" ,c + dt",e + ft), where a, b, c, d, e, and f are real numbers and p is a positive integer, has zero curvature. Give an explanation What must be shown to prove that r(t) has zero curvature? OA. It must be shown that the velocity, v, and the acceleration, a, are constant. GB. It must be shown that the magnitude of the cross product, axv, is zero, or that the unit tangent vector, T, is constant. OC. It must be shown that the cross product a xv is constant. O D. It must be shown that the dot product, a v, is zero, or that the acceleration, a, is constant. In this problem, show that the magnitude of the cross product, axv, is zero. To do so, first find the velocity, v. {a + bt,c+ dtP,e + ftP}arrow_forwardA curve in space is represented as a function of a parameter, 1, by the position vector r(t) = [3sin 2t , 3cos 21 , 81]. At a general point on the curve, derive expressions for the unit tangent vector, the unit principle normal vector, the unit bi-normal vector and curvature. Q1. (a)arrow_forward
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