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Home » Question: In spherical coordinates, a surface is defined by $ - DevRocket

Question: In spherical coordinates, a surface is defined by $ - DevRocket

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Volume of a hemisphere of radius $ 3r $ is half the volume of a full sphere of that radius:

📌 Question: A materials scientist models a crystal lattice with a regular tetrahedron. Three vertices are at $(1, 2, 3)$, $(4, 5, 6)$, and $(7, 8, 9)$. Find the integer coordinates of the fourth vertex.

📌 Solution: The centroid of a regular tetrahedron is the average of its vertices. Let the fourth vertex be $(x, y, z)$. The centroid is:

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