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HMMT 二月 2001 · 几何 · 第 5 题

HMMT February 2001 — Geometry — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find the volume of the tetrahedron with vertices (5 , 8 , 10) , (10 , 10 , 17) , (4 , 45 , 46) , (2 , 5 , 4).
解析
  1. Find the volume of the tetrahedron with vertices (5 , 8 , 10) , (10 , 10 , 17) , (4 , 45 , 46) , (2 , 5 , 4). Solution: Each vertex ( x, y, z ) obeys x + y = z + 3, so all the vertices are coplanar and the volume of the tetrahedron is 0 .