Consider the function h(x, y, z) = x² - 2y² + 3z², = and its level surface S through the point (1, 1, 1). Determine the shortest distance from S to the origin by considering the function f(x, y, z) x² + y² + z² and writing down the Lagrangian for finding the minimum of f subject to (x, y, z) lying on S. Determine the critical points and by comparison of the values of fat these points determine the minimum distance.

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