Consider the curve given by z(t) = (t, t², 1) for 0 ≤t≤ 1. Find a parametrization of the (orthognal) projection of this curve onto the plane x + y + z = 0. Calculate the average distance of the curve a to the plane. Hint: Do not forget the arc-length element when you set up the integral. Explain why the integral you setup is the correct one.

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