设A（x1,y1,z1）,B（x2,y2,z2）,C（x3,y3,z3）则属于平面内的向量AB（x2-x1,y2-y1,z2-z1）,AC(x3-x1,y3-y1,z3-z1)则平面方程为| x y z | |x2-x1 y2-y1 z2-z1|=0 |x3-x1 y3-y1 z3-z1|有：x[(y2-y1)(z3-z1)-(z2-z1)(y3-y1)]-y[(x2-x1)(z3-z1)-(z2-z1)(x3-x1)]+z[(x2-x1)(y3-y1)-(y2-y1)(x3-x1)]=0