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How Can I Sign a Word Document - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 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 $.

📌 Thus, the fourth vertex is $ (0,2,2) $. Verify distances:

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