The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. We want to find the points on the ellipse that lie closest to the origin. Using Lagrange Multiplier method, set up a system of equations for such points. Need not solve it. Hint: Let (x, y, z) be the point on the ellipse. Then the goal is to minimize f(x, y, z) = x2 + y2 + z2 (= square of the distance from the origin), under a constraint. Write the constraint function clearly,