6. Consider the path given by r(t) = (cost, cost sint, sin² t), 0 ≤ t ≤ 2π. (a) Show that the path is a parameterization of a curve that lies on the unit sphere. (b) Find a parametrization of the line tangent to the curve when t = π/2. (c) Show that the path is a parameterization of a curve that lies on the parabolic cylinder z = 1-x².

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