Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ −12x₁ x3 +24X2X3. Find a unit vector x in R³ at which Q(x) is maximized, subject to xJx=1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]

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