Solved via determinants

planes.cpp

@@ -0,0 +1,53 @@
+#include <iostream>
+#include <math.h>
+
+using namespace std;
+
+typedef struct Points 
+{
+	int x;
+	int y;
+	int z;
+} Points; 
+
+int main()
+{
+	int testNum;
+	cin >> testNum;
+
+	while(testNum--){
+		Points point1, point2, point3, point4;
+		cin >> point1.x >> point1.y >> point1.z;
+		cin >> point2.x >> point2.y >> point2.z;
+		cin >> point3.x >> point3.y >> point3.z;
+		cin >> point4.x >> point4.y >> point4.z;
+
+		Points vector1;
+		vector1.x = point2.x - point1.x;
+		vector1.y = point2.y - point1.y;
+		vector1.z = point2.z - point1.z;
+
+		Points vector2;
+		vector2.x = point3.x - point1.x;
+		vector2.y = point3.y - point1.y;
+		vector2.z = point3.z - point1.z;
+
+		Points vector3;
+		vector3.x = point4.x - point1.x;
+		vector3.y = point4.y - point1.y;
+		vector3.z = point4.z - point1.z;
+
+		int deter1 = vector1.x * ((vector2.y * vector3.z) - (vector3.y * vector2.z));
+		int deter2 = vector2.x * ((vector1.y * vector3.z) - (vector3.y * vector1.z));
+		int deter3 = vector3.x * ((vector1.y * vector2.z) - (vector2.y * vector1.z));
+
+		int result = deter1 - deter2 + deter3;
+		if(result == 0){
+			cout << "YES" << endl;
+		} else {
+			cout << "NO" << endl;
+		}
+	}
+
+	return 0;
+}