Determine whether the following trajectories lie on a circle in R 2 or sphere in R 3

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Determine whether the following trajectories lie on a circle in R2 or sphere in R3 centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the velocity vector are everywhere orthogonal.

r(t) = (3 sin t, 5 cos t, 4 sin t), for 0 ≤ t ≤ 2π

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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