Question: Consider the ellipsoid E defined by x^2 + 2y^2 + 3z^2 = 6. (a) Find the equation of the plane P tangent to the ellipsoid

Consider the ellipsoid E defined by x^2 + 2y^2 + 3z^2 = 6.

(a) Find the equation of the plane P tangent to the ellipsoid E at (1, 1, 1).

(b) Find the point on the plane P nearest to the origin (0, 0, 0).

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