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- Find the length of the curve r(t) = (2t3/2, cos 3t, sin 3t) from 0 to 3.A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t sin 2t. Find the speed of the particle when t = /2.1. For the curve given by R(t) = (cost + tsin t)i + (sin t − t cost)j + (t^2)k, find a. the length of arc from t = 0 to t = 2π, andb. the moving trihedral for t > 0.