# Program to find equation of a plane passing through 3 points in C++

In this tutorial, we will be discussing a program to find equation of a plane passing through 3 points.

For this we will be provided with 3 points. Our task is to find the equation of the plane consisting of or passing through those three given points.

## Example

Live Demo

#include <bits/stdc++.h>
#include<math.h>
#include <iostream>
#include <iomanip>
using namespace std;
//finding the equation of plane
void equation_plane(float x1, float y1, float z1, float x2, float y2, float z2, float x3, float y3, float z3){
float a1 = x2 - x1;
float b1 = y2 - y1;
float c1 = z2 - z1;
float a2 = x3 - x1;
float b2 = y3 - y1;
float c2 = z3 - z1;
float a = b1 * c2 - b2 * c1;
float b = a2 * c1 - a1 * c2;
float c = a1 * b2 - b1 * a2;
float d = (- a * x1 - b * y1 - c * z1);
std::cout << std::fixed;
std::cout << std::setprecision(2);
cout << "Equation of plane is " << a << " x + " << b << " y + " << c << " z + " << d << " = 0";
}
int main(){
float x1 =-1;
float y1 = 2;
float z1 = 1;
float x2 = 0;
float y2 =-3;
float z2 = 2;
float x3 = 1;
float y3 = 1;
float z3 =-4;
equation_plane(x1, y1, z1, x2, y2, z2, x3, y3, z3);
return 0;
}

## Output

Equation of plane is 26.00 x + 7.00 y + 9.00 z + 3.00 = 0