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Home » + 50x + 20x + 4x^2 = 600 - RTA

+ 50x + 20x + 4x^2 = 600 - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 Question: A research scientist designs a crystal lattice where three vertices of a regular tetrahedron are at $ (0,0,0) $, $ (2,2,0) $, and $ (2,0,2) $. If the fourth vertex has integer coordinates, find its location.

📌 Solution: Let the fourth vertex be $ D = (x, y, z) $, and denote $ A = (0,0,0) $, $ B = (2,2,0) $, $ C = (2,0,2) $. In a regular tetrahedron, all edges have equal length.

📌 From (1): $ y = 2 - x $, from (2): $ z = 2 - x $.

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