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The problem of the rate region of the vector Gaussian multiple description with individual and central quadratic distortion constraints is studied. We have two main contributions. First, a lower bound on the rate region is derived. The bound is obtained by lower-bounding a weighted sum rate for each supporting hyperplane of the rate region. Second, the rate region for the scenario of the scalar Gaussian source is fully characterized by showing that the lower bound is tight. The optimal weighted sum rate for each supporting hyperplane is obtained by solving a single maximization problem. This is contrary to existing results, which require solving a min-max optimization problem.