三角形有重心、内心、旁心,国内外不少作者都研究从事过类比研究,即把三角形的这三“心”——重心、内心、旁心移植到四面体(即三棱锥)中,并且给出相应的性质[1]-[2].本文从向量的角度,给出四面体中三“心”——重心、内心、旁心的一种判断方法.1.四面体的重心的判定由三角形的一个顶点与对边的中点为端点确定的线段称为三角形的中线,三角形的三条中线交于一点(此点称为三角形的重心),且这点是顶点与对 The triangle has a center of gravity, an inner heart, and an adjacent heart. Many authors both at home and abroad have studied analogy, that is, transplanting the three “hearts” of the triangle—the center of gravity, the heart, and the center of the heart—into a tetrahedron (ie, a triangular pyramid). , and give the corresponding properties [1]-[2]. This paper gives a method of judging the center of gravity, inner heart, and the center of the heart in a tetrahedron from the perspective of a vector. 1. tetrahedron The determination of the center of gravity consists of a line segment defined by a vertex of the triangle and the midpoint of the opposite side as the midline of the triangle. The three midlines of the triangle intersect at a point (this point is called the center of gravity of the triangle), and this is the vertex and pair