Word Count : 396

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We are tasked with finding the transformation of the given equation under a specific rotation of axes. The original equation is: \[ 12x^2 - 2y^2 + z^2 = 2xy \] The new axes have direction ratios given by the vectors: 1. \( \mathbf{a}_1 = (1, -3, 0) \) 2. \( \mathbf{a}_2 = (3, 1, 0) \) 3. \( \mathbf{a}_3 = (0, 0, 1) \) These direction ratios suggest that the new coordinate system can be described by a rotation ________ ________ _________ _____ _____ _________ _____.
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