Data Modelling & AI Data Structure & Algorithm

Program to find X, Y and Z intercepts of a plane

23 June 2025

0

In this article, it is explained how to find the X, Y, and Z intercepts of a plane. There are two ways to find the intercepts:

Case 1: When the general equation of the plane is given.

Examples:

Input: A = -6, B = 5, C = -3, D = 9 
Output:
1.5 
-1.8 
3.0

Input: A = 7, B = 4, C = 5, D = -7 
Output: 
1.0 
1.75 
1.4

Approach:

The result can be computed by following the below steps:

Convert general equation of a plane Ax + By + Cz + D = 0 to Ax + By + Cz = – D
Divide by -D into both sides of the equation
So, the equation becomes x/(-D/A) + y/(-D/B) + z(-D/C) = 1
The above equation is in the intercept form of a plane. Therefore,
X intercepts will be = -D/A
Y intercepts will be = -D/B
Z intercepts will be = -D/C

Below is the implementation of the above approach:

C++

// C++ program to find the 
// X, Y and Z intercepts of a plane
#include<iostream>
using namespace std;
 
float * XandYandZintercept(float A, float B,
                            float C, float D)
{
        static float rslt[3];
         
        // For finding the x-intercept 
        // put y = 0 and z = 0 
        float x = -D / A ;
     
        // For finding the y-intercept 
        // put x = 0 and z = 0 
        float y = -D / B ;
     
        // For finding the z-intercept 
        // put x = 0 and y = 0 
        float z = -D / C ;
         
        rslt[0] = x;
        rslt[1] = y;
        rslt[2] = z;
         
        return rslt; 
}
     
// Driver code 
int main () 
{
    int A = 2 ;
    int B = 5 ;
    int C = 7;
    int D = 8 ;
         
    float *rslt = XandYandZintercept(A, B, C, D);
         
    for(int i = 0; i < 3 ; i++)
    {
        cout << rslt[i] << " ";
    }
     
}
 
// This code is contributed by ANKITKUMAR34

Java

// Java program to find the 
// X, Y and Z intercepts of a plane
class GFG 
{
     
    static float[] XandYandZintercept(float A, 
                    float B, float C, float D)
    {
        float rslt[] = new float[3];
         
        // For finding the x-intercept 
        // put y = 0 and z = 0 
        float x = -D / A ;
     
        // For finding the y-intercept 
        // put x = 0 and z = 0 
        float y = -D / B ;
     
        // For finding the z-intercept 
        // put x = 0 and y = 0 
        float z = -D / C ;
         
        rslt[0] = x;
        rslt[1] = y;
        rslt[2] = z;
         
        return rslt; 
    }
     
    // Driver code 
    public static void main (String[] args) 
    {
        int A = 2 ;
        int B = 5 ;
        int C = 7;
        int D = 8 ;
         
        float rslt[] = XandYandZintercept(A, B, C, D);
         
        for(int i = 0; i < 3 ; i++)
        {
            System.out.print(rslt[i] + " ");
        }
    }
}
 
// This code is contributed by AnkitRai01

Python3

# Python program to find the 
# X, Y and Z intercepts of a plane
 
def XandYandZintercept(A, B, C, D): 
 
    # For finding the x-intercept 
    # put y = 0 and z = 0
    x = -D / A
 
    # For finding the y-intercept 
    # put x = 0 and z = 0 
    y = -D / B 
 
    # For finding the z-intercept 
    # put x = 0 and y = 0
    z = -D / C
    return [x, y, z]
 
# Driver code
A = 2
B = 5
C = 7
D = 8
print(XandYandZintercept(A, B, C, D))

C#

// C# program to find the 
// X, Y and Z intercepts of a plane
using System;
 
class GFG 
{
     
    static float[] XandYandZintercept(float A, 
                    float B, float C, float D)
    {
        float []rslt = new float[3];
         
        // For finding the x-intercept 
        // put y = 0 and z = 0 
        float x = -D / A ;
     
        // For finding the y-intercept 
        // put x = 0 and z = 0 
        float y = -D / B ;
     
        // For finding the z-intercept 
        // put x = 0 and y = 0 
        float z = -D / C ;
         
        rslt[0] = x;
        rslt[1] = y;
        rslt[2] = z;
         
        return rslt; 
    }
     
    // Driver code 
    public static void Main() 
    {
        int A = 2 ;
        int B = 5 ;
        int C = 7;
        int D = 8 ;
         
        float []rslt = XandYandZintercept(A, B, C, D);
         
        for(int i = 0; i < 3 ; i++)
        {
            Console.Write(rslt[i] + " ");
        }
    }
}
 
// This code is contributed by AnkitRai01

Javascript

<script>
      // JavaScript program to find the
      // X, Y and Z intercepts of a plane
 
      function XandYandZintercept(A, B, C, D) {
        // For finding the x-intercept
        // put y = 0 and z = 0
        var x = -D / A;
 
        // For finding the y-intercept
        // put x = 0 and z = 0
        var y = -D / B;
 
        // For finding the z-intercept
        // put x = 0 and y = 0
        var z = -D / C;
        return [x, y, z];
      }
      function equation_plane(p, q, r) {
        var x1 = p[0];
        var y1 = p[1];
        var z1 = p[2];
        var x2 = q[0];
        var y2 = q[1];
        var z2 = q[2];
        var x3 = r[0];
        var y3 = r[1];
        var z3 = r[2];
 
        // For Finding value of A, B, C, D
        var a1 = x2 - x1;
        var b1 = y2 - y1;
        var c1 = z2 - z1;
        var a2 = x3 - x1;
        var b2 = y3 - y1;
        var c2 = z3 - z1;
        var A = b1 * c2 - b2 * c1;
        var B = a2 * c1 - a1 * c2;
        var C = a1 * b2 - b1 * a2;
        var D = -A * x1 - B * y1 - C * z1;
 
        // Calling the first created function
 
        var [x, y, z] = XandYandZintercept(A, B, C, D);
        document.write(x + " " + y + " " + z);
      }
      // Driver Code
      var x1 = -1;
      var y1 = 2;
      var z1 = 1;
      var x2 = 0;
      var y2 = -3;
      var z2 = 2;
      var x3 = 1;
      var y3 = 1;
      var z3 = -4;
 
      var p = [x1, y1, z1];
      var q = [x2, y2, z2];
      var r = [x3, y3, z3];
 
      equation_plane(p, q, r);
    </script>

Output:

[-4.0, -1.6, -1.1428571428571428]

Time Complexity: O(1)

Auxiliary Space: O(1)

Case 2: When 3 non-collinear points are given.

Examples:

Input: A = (3, 17, 2), B = (4, 8, 5), C = (1, 8, 3) 
Output:
1.5 
-1.8 
3.0

Input: A = (2, 11, 4), B = (7, 8, 3), C = (9, 18, 23) 
Output: 
1.0 
1.75 
1.4

Approach:

The idea is to find the Cartesian form of the equation using three points.

When three points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) are given, the determinant value of the following matrix gives the Cartesian form.
| (x – x1) (y – y1) (z – z1) |
| (x2 – x1) (y2 – y1) (z2 – z1)| = 0
| (x3 – x1) (y3 – y1) (z3 – z1)|
Once the above determinant is found, then the intercepts can be found using the first mentioned approach.

Below is the implementation of the above approach:

C++

// C++ program to find the 
// X, Y and Z intercepts of a plane
#include<bits/stdc++.h>
using namespace std;
 
float * XandYandZintercept( float A, float B, 
                            float C, float D)
{
    static float rslt[3];
     
    // For finding the x-intercept 
    // put y = 0 and z = 0
    float x = -D / A;
 
    // For finding the y-intercept 
    // put x = 0 and z = 0 
    float y = -D / B ;
 
    // For finding the z-intercept 
    // put x = 0 and y = 0
    float z = -D / C;
    rslt[0] = x;
    rslt[1] = y;
    rslt[2] = z; 
     
    return rslt;
}
 
void equation_plane(int p[], int q[], int r[])
{
    int x1 = p[0];
    int y1 = p[1];
    int z1 = p[2];
    int x2 = q[0];
    int y2 = q[1];
    int z2 = q[2];
    int x3 = r[0];
    int y3 = r[1];
    int z3 = r[2];
     
    // For Finding value of A, B, C, D
    int a1 = x2 - x1;
    int b1 = y2 - y1;
    int c1 = z2 - z1;
    int a2 = x3 - x1;
    int b2 = y3 - y1;
    int c2 = z3 - z1;
    int A = b1 * c2 - b2 * c1;
    int B = a2 * c1 - a1 * c2;
    int C = a1 * b2 - b1 * a2;
    int D = (- A * x1 - B * y1 - C * z1);
     
    // Calling the first created function 
    float * rslt=XandYandZintercept(A, B, C, D); 
    for(int i = 0; i < 3; i++)
    {
        cout << rslt[i] << " ";
    }
}
     
// Driver Code 
int main() 
{
    int x1 =-1;
    int y1 = 2;
    int z1 = 1;
    int x2 = 0;
    int y2 =-3;
    int z2 = 2;
    int x3 = 1;
    int y3 = 1;
    int z3 =-4;
         
    int p[3] = {x1, y1, z1};
    int q[3] = {x2, y2, z2};
    int r[3] = {x3, y3, z3};
    equation_plane(p, q, r);
 
}
 
// This code is contributed by chitranayal

Java

// Java program to find the 
// X, Y and Z intercepts of a plane
import java.util.*;
 
class solution{
 
static double[] XandYandZintercept( double A, double B, 
                            double C, double D)
{
    double []rslt = new double[3];
     
    // For finding the x-intercept 
    // put y = 0 and z = 0
    double x = -D / A;
 
    // For finding the y-intercept 
    // put x = 0 and z = 0 
    double y = -D / B ;
 
    // For finding the z-intercept 
    // put x = 0 and y = 0
    double z = -D / C;
    rslt[0] = x;
    rslt[1] = y;
    rslt[2] = z; 
     
    return rslt;
}
 
static void equation_plane(int []p, int []q, int []r)
{
    int x1 = p[0];
    int y1 = p[1];
    int z1 = p[2];
    int x2 = q[0];
    int y2 = q[1];
    int z2 = q[2];
    int x3 = r[0];
    int y3 = r[1];
    int z3 = r[2];
     
    // For Finding value of A, B, C, D
    int a1 = x2 - x1;
    int b1 = y2 - y1;
    int c1 = z2 - z1;
    int a2 = x3 - x1;
    int b2 = y3 - y1;
    int c2 = z3 - z1;
    int A = b1 * c2 - b2 * c1;
    int B = a2 * c1 - a1 * c2;
    int C = a1 * b2 - b1 * a2;
    int D = (- A * x1 - B * y1 - C * z1);
     
    // Calling the first created function 
    double []rslt = XandYandZintercept(A, B, C, D);
    for(int i = 0; i < 3; i++)
    {
        System.out.printf(rslt[i]+" ");
    }
}
     
// Driver Code 
public static void main(String args[]) 
{
    int x1 =-1;
    int y1 = 2;
    int z1 = 1;
    int x2 = 0;
    int y2 =-3;
    int z2 = 2;
    int x3 = 1;
    int y3 = 1;
    int z3 =-4;
         
    int []p = {x1, y1, z1};
    int []q = {x2, y2, z2};
    int []r = {x3, y3, z3};
    equation_plane(p, q, r);
 
}
}
 
// This code is contributed by Surendra_Gangwar

Python3

# Python program to find the 
# X, Y and Z intercepts of a plane
 
def XandYandZintercept(A, B, C, D): 
  
    # For finding the x-intercept 
    # put y = 0 and z = 0
    x = -D / A
 
    # For finding the y-intercept 
    # put x = 0 and z = 0 
    y = -D / B 
 
    # For finding the z-intercept 
    # put x = 0 and y = 0
    z = -D / C
    return [x, y, z]
  
def equation_plane(p, q, r): 
    x1 = p[0]
    y1 = p[1]
    z1 = p[2]
    x2 = q[0]
    y2 = q[1]
    z2 = q[2]
    x3 = r[0]
    y3 = r[1]
    z3 = r[2]
     
    # For Finding value of A, B, C, D
    a1 = x2 - x1
    b1 = y2 - y1
    c1 = z2 - z1
    a2 = x3 - x1
    b2 = y3 - y1
    c2 = z3 - z1
    A = b1 * c2 - b2 * c1
    B = a2 * c1 - a1 * c2
    C = a1 * b2 - b1 * a2
    D = (- A * x1 - B * y1 - C * z1)
     
    # Calling the first created function 
    print(XandYandZintercept(A, B, C, D)) 
     
# Driver Code 
x1 =-1
y1 = 2
z1 = 1
x2 = 0
y2 =-3
z2 = 2
x3 = 1
y3 = 1
z3 =-4
 
equation_plane((x1, y1, z1), (x2, y2, z2), (x3, y3, z3))

C#

// C# program to find the  
// X, Y and Z intercepts of a plane 
using System;
class GFG{
     
static double[] XandYandZintercept(double A, 
                                   double B,  
                                   double C, 
                                   double D) 
{ 
  double[] rslt = new double[3]; 
 
  // For finding the x-intercept  
  // put y = 0 and z = 0 
  double x = -D / A; 
 
  // For finding the y-intercept  
  // put x = 0 and z = 0  
  double y = -D / B ; 
 
  // For finding the z-intercept  
  // put x = 0 and y = 0 
  double z = -D / C; 
  rslt[0] = x; 
  rslt[1] = y; 
  rslt[2] = z;  
 
  return rslt; 
} 
 
static void equation_plane(int[] p, 
                           int[] q, 
                           int[] r) 
{ 
  int x1 = p[0]; 
  int y1 = p[1]; 
  int z1 = p[2]; 
  int x2 = q[0]; 
  int y2 = q[1]; 
  int z2 = q[2]; 
  int x3 = r[0]; 
  int y3 = r[1]; 
  int z3 = r[2]; 
 
  // For Finding value 
  // of A, B, C, D 
  int a1 = x2 - x1; 
  int b1 = y2 - y1; 
  int c1 = z2 - z1; 
  int a2 = x3 - x1; 
  int b2 = y3 - y1; 
  int c2 = z3 - z1; 
  int A = (b1 * c2 - 
           b2 * c1); 
  int B = (a2 * c1 - 
           a1 * c2); 
  int C = (a1 * b2 - 
           b1 * a2); 
  int D = (- A * x1 - 
           B * y1 - 
           C * z1); 
 
  // Calling the first 
  // created function  
  double[] rslt = XandYandZintercept(A, B, 
                                     C, D); 
  for(int i = 0; i < 3; i++) 
  { 
    Console.Write(rslt[i] + " "); 
  } 
} 
 
// Driver code
static void Main() 
{
  int x1 =-1; 
  int y1 = 2; 
  int z1 = 1; 
  int x2 = 0; 
  int y2 =-3; 
  int z2 = 2; 
  int x3 = 1; 
  int y3 = 1; 
  int z3 =-4; 
 
  int[] p = {x1, y1, z1}; 
  int[] q = {x2, y2, z2}; 
  int[] r = {x3, y3, z3}; 
  equation_plane(p, q, r); 
}
}
 
// This code is contributed by divyeshrabadiya07

Javascript

<script>
 
// Javascript program to find the
// X, Y and Z intercepts of a plane
function XandYandZintercept(A, B, C, D)
{
    let rslt = new Array(3);
     
    // For finding the x-intercept
    // put y = 0 and z = 0
    let x = -D / A;
  
    // For finding the y-intercept
    // put x = 0 and z = 0
    let y = -D / B ;
  
    // For finding the z-intercept
    // put x = 0 and y = 0
    let z = -D / C;
    rslt[0] = x;
    rslt[1] = y;
    rslt[2] = z;
      
    return rslt;
}
 
function equation_plane(p, q, r)
{
    let x1 = p[0];
    let y1 = p[1];
    let z1 = p[2];
    let x2 = q[0];
    let y2 = q[1];
    let z2 = q[2];
    let x3 = r[0];
    let y3 = r[1];
    let z3 = r[2];
      
    // For Finding value of A, B, C, D
    let a1 = x2 - x1;
    let b1 = y2 - y1;
    let c1 = z2 - z1;
    let a2 = x3 - x1;
    let b2 = y3 - y1;
    let c2 = z3 - z1;
    let A = b1 * c2 - b2 * c1;
    let B = a2 * c1 - a1 * c2;
    let C = a1 * b2 - b1 * a2;
    let D = (- A * x1 - B * y1 - C * z1);
     
    // Calling the first created function
    let rslt = XandYandZintercept(A, B, C, D);
    for(let i = 0; i < 3; i++)
    {
        document.write(rslt[i] + " ");
    }
}
 
// Driver Code
let x1 = -1;
let y1 = 2;
let z1 = 1;
let x2 = 0;
let y2 = -3;
let z2 = 2;
let x3 = 1;
let y3 = 1;
let z3 = -4;
 
let p = [ x1, y1, z1 ];
let q = [ x2, y2, z2 ];
let r = [ x3, y3, z3 ];
 
equation_plane(p, q, r);
 
// This code is contributed by rag2127
 
</script>

Output:

[-0.11538461538461539, -0.42857142857142855, -0.3333333333333333]

Time Complexity: O(1), Space Complexity: O(1)

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Program to find X, Y and Z intercepts of a plane

Case 1: When the general equation of the plane is given.

Approach:

C++

Java

Python3

C#

Javascript

Case 2: When 3 non-collinear points are given.

Approach:

C++

Java

Python3

C#

Javascript

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