Compute Curva ture and torsion Of (x)t = ( 3t - t, 3t², 3e+t³) %3D Show trat it is helix . (Find arclength, and a construct Frenet Frame, Find sphericai image involude and evolute, Find ourvature and torsions of involute).

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Find the curvature of rt)%3D point (2,0, /3) I1> (t)= 9C00(3t), 0 k4.0%2)

a parametric position vector is defined as pictured - the final condition makes sure of a positive radius plots show space curves for the pos. vector alpha = 3, beta = 1, k = 2, h = 4, and w = 1. cylindrical vector definitions x = p cos(phi), y = psin(phi), z = z , p = sqrt(x^2+y^2), phi = arctan(y/x) a) find when the velocity vector r'(t) is perpendicular to the position vector (pictured) b) simplify the answer to a) for the parameter values used to construct the space curve in thefigure. Is the result consistent with the space curve?