四个点构造三个向量，形成一个行列式 若行列式的值为0，则共面；不为0，则不共面
#include<iostream> #include<cstdio> #include<cstring> #include<algorithm> #include<string> using namespace std; struct Point { int x,y,z; } p[5]; int main() { int t; scanf("%d",&t); while(t--) { for(int i=0; i<4; i++) scanf("%d %d %d",&p[i].x,&p[i].y,&p[i].z); Point s1,s2,s3; s1.x=p[1].x-p[0].x; s1.y=p[1].y-p[0].y; s1.z=p[1].z-p[0].z; s2.x=p[2].x-p[0].x; s2.y=p[2].y-p[0].y; s2.z=p[2].z-p[0].z; s3.x=p[3].x-p[0].x; s3.y=p[3].y-p[0].y; s3.z=p[3].z-p[0].z; int ans; ans=s1.x*s2.y*s3.z+s1.y*s2.z*s3.x+s1.z*s2.x*s3.y-s1.z*s2.y*s3.x-s1.x*s2.z*s3.y-s1.y*s2.x*s3.z; if(ans==0) puts("Yes"); else puts("No"); } }