文[1]给出三角形重心的一个向量性质,并向三棱锥进行了拓广.受其启发,笔者得到了三角形内心和旁心的一个向量性质及其空间拓广形式.定理1如图1,已知a,b,c是△ABC的角A,B,C的对边,l为△ABC的周长,点O是△ABC的内心,P为△ABC内一点,直线PO与BC,CA,AB所在直线分别交于D,E,F点,且DP In [1], we give a vector property of the triangle center of gravity and expand it to a triangular pyramid. Inspired by it, the author obtains a vector property of the triangle’s inner and side centers and its spatial extension form. Theorem 1 is shown in Figure 1. Knowing that a, b, and c are the angles A, B, and C of △ABC, l is the circumference of △ABC, point O is the inside of △ABC, P is the point within △ABC, and the lines PO and BC, CA, AB are on the straight line respectively at points D, E, F, and DP