51nod 1265 四点共面（判四点共面）

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>

#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)

using namespace std;

struct point3{
    double x,y,z;
};

struct line3{
    point3 a,b;
};

struct plane3{
    point3 a,b,c;
};

point3 xmult(point3 u,point3 v){
    point3 ret;
    ret.x = u.y*v.z - v.y*u.z;
    ret.y = u.z*v.x - u.x*v.z;
    ret.z = u.x*v.y - u.y*v.x;
    return ret;
}

point3 subt(point3 u,point3 v){
    point3 ret;
    ret.x = u.x - v.x;
    ret.y = u.y - v.y;
    ret.z = u.z - v.z;
    return ret;
}

point3 pvec(point3 a,point3 b,point3 c){
    return xmult(subt(a,b),subt(b,c));
}

double dmult(point3 u,point3 v){
    return u.x*v.x + u.y*v.y + u.z*v.z;
}

int dots_onplane(point3 a,point3 b,point3 c,point3 d){
    return zero(dmult(pvec(a,b,c),subt(d,a)));
}

int main(){
    point3 a[4];
    int T;
    scanf("%d",&T);
    while(T--){
        for(int i=0;i<4;i++){
            scanf("%lf%lf%lf",&a[i].x,&a[i].y,&a[i].z);
        }
        int flag = dots_onplane(a[0],a[1],a[2],a[3]);
        if(flag == 1){
            printf("Yes\n");
        }else{
            printf("No\n");
        }
    }
    return 0;
}