Skip to content
Related Articles

Related Articles

Check if the given vectors are at equilibrium or not
  • Last Updated : 20 Apr, 2021

Given the x, y and z coordinates of three vectors, the task is to check if they are at equilibrium or not.
Examples: 
 

Input: x1 = -2, y1 = 1, z1 = 0, x2 = 5, y2 = 0, z2 = 5, x3 = -3, y3 = -1, z3 = -5 
Output: The vectors are at equilibrium.
Input: x1 = 2, y1 = -17, z1 = 0, x2 = 5, y2 = 1, z2 = -5, x3 = 4, y3 = 2, z3 = -4 
Output: The vectors are not at equilibrium.

 

When Three vectors are at equilibrium 
 



Approach: Three vectors are at equilibrium when the results of those three vectors is a Null vector, i.e. it has no magnitude and direction. Resultant of three vectors is equal to the vector sum of the vectors. The resultant vector is Null when, ∑x = 0, ∑y = 0 and ∑ z = 0. Thus we can say that when the said condition satisfies then the vectors are at equilibrium and otherwise not.
 

C++




// CPP program to check the equlibrium of three vectors
#include <bits/stdc++.h>
using namespace std;
 
// Function to check the equlibrium of three vectors
bool checkEqulibrium(int x1, int y1, int z1, int x2, int y2,
                     int z2, int x3, int y3, int z3)
{
 
    // summing the x coordinates
    int resx = x1 + x2 + x3;
 
    // summing the y coordinates
    int resy = y1 + y2 + y3;
 
    // summing the z coordinates
    int resz = z1 + z2 + z3;
 
    // Checking the condition for equlibrium
    if (resx == 0 and resy == 0 and resz == 0)
        return true;
    else
        return false;
}
 
// Driver code
int main()
{
    int x1 = -2, y1 = -7, z1 = -9, x2 = 5, y2 = -14, z2 = 14,
        x3 = -3, y3 = 21, z3 = -5;
 
    // Checking for equlibrium
    if (checkEqulibrium(x1, y1, z1, x2, y2, z2, x3, y3, z3))
        cout << "The vectors are at equilibrium.";
    else
        cout << "The vectors are not at equilibrium.";
 
    return 0;
}

Java




// Java program to check the equilibrium of three vectors
 
public class GFG {
 
    // Function to check the equilibrium of three vectors
    static boolean checkEqulibrium(int x1, int y1, int z1, int x2, int y2,
                        int z2, int x3, int y3, int z3)
    {
 
        // summing the x coordinates
        int resx = x1 + x2 + x3;
 
        // summing the y coordinates
        int resy = y1 + y2 + y3;
 
        // summing the z coordinates
        int resz = z1 + z2 + z3;
 
        // Checking the condition for equilibrium
        if (resx == 0 & resy == 0 & resz == 0)
            return true;
        else
            return false;
    }
 
 
    // Driver code
    public static void main(String args[])
    {
        int x1 = -2, y1 = -7, z1 = -9, x2 = 5, y2 = -14,
              z2 = 14, x3 = -3, y3 = 21, z3 = -5;
 
                // Checking for equlibrium
                if (checkEqulibrium(x1, y1, z1, x2, y2,
                                    z2, x3, y3, z3))
                    System.out.println("The vectors are at equilibrium.");
                else
                    System.out.println("The vectors are not at equilibrium.");
 
    }
     
}
// This code is contributed by ANKITRAI1

Python 3




# Python 3 program to check the
# equlibrium of three vectors
 
# Function to check the equlibrium
# of three vectors
def checkEqulibrium(x1, y1, z1, x2, y2,
                    z2, x3, y3, z3) :
 
    # summing the x coordinates
    resx = x1 + x2 + x3
 
    # summing the y coordinates
    resy = y1 + y2 + y3
 
    # summing the z coordinates
    resz = z1 + z2 + z3
 
    # Checking the condition for equlibrium
    if (resx == 0 and resy == 0 and
                      resz == 0):
        return True
    else:
        return False
 
# Driver code
x1 = -2; y1 = -7; z1 = -9
x2 = 5; y2 = -14; z2 = 14
x3 = -3; y3 = 21; z3 = -5
 
# Checking for equlibrium
if (checkEqulibrium(x1, y1, z1,
                    x2, y2, z2,
                    x3, y3, z3)):
    print("The vectors are at equilibrium.")
     
else:
    print("The vectors are not at equilibrium.")
 
# This code is contributed
# by Akanksha Rai

C#




// C# program to check the equilibrium
// of three vectors
class GFG
{
 
// Function to check the equilibrium
// of three vectors
static bool checkEqulibrium(int x1, int y1, int z1,
                            int x2, int y2,    int z2,
                            int x3, int y3, int z3)
{
 
    // summing the x coordinates
    int resx = x1 + x2 + x3;
 
    // summing the y coordinates
    int resy = y1 + y2 + y3;
 
    // summing the z coordinates
    int resz = z1 + z2 + z3;
 
    // Checking the condition for equilibrium
    if (resx == 0 & resy == 0 & resz == 0)
        return true;
    else
        return false;
}
 
// Driver code
public static void Main()
{
    int x1 = -2, y1 = -7, z1 = -9,
        x2 = 5, y2 = -14, z2 = 14,
        x3 = -3, y3 = 21, z3 = -5;
 
    // Checking for equlibrium
    if (checkEqulibrium(x1, y1, z1, x2, y2,
                        z2, x3, y3, z3))
        System.Console.WriteLine("The vectors are " +
                                  "at equilibrium.");
    else
        System.Console.WriteLine("The vectors are not " +
                                      "at equilibrium.");
 
}
}
 
// This code is contributed by mits

PHP




<?php
// PHP program to check the equlibrium
// of three vectors
 
// Function to check the equlibrium
// of three vectors
function checkEqulibrium($x1, $y1, $z1,
                         $x2, $y2, $z2,
                         $x3, $y3, $z3)
{
 
    // summing the x coordinates
    $resx = $x1 + $x2 + $x3;
 
    // summing the y coordinates
    $resy = $y1 + $y2 + $y3;
 
    // summing the z coordinates
    $resz = $z1 + $z2 + $z3;
 
    // Checking the condition
    // for equlibrium
    if ($resx == 0 and $resy == 0 and
                       $resz == 0)
        return true;
    else
        return false;
}
 
// Driver code
$x1 = -2; $y1 = -7; $z1 = -9;
$x2 = 5; $y2 = -14; $z2 = 14;
$x3 = -3; $y3 = 21; $z3 = -5;
 
// Checking for equlibrium
if (checkEqulibrium($x1, $y1, $z1,
                    $x2, $y2, $z2,
                    $x3, $y3, $z3))
    echo "The vectors are at equilibrium.";
else
    echo "The vectors are not at equilibrium.";
 
// This code is contributed by akt_mit
?>

Javascript




<script>
 
// Javascript program to check the
// equilibrium of three vectors
 
// Function to check the equilibrium
// of three vectors
function checkEqulibrium(x1, y1, z1, x2, y2,
                         z2, x3, y3, z3)
{
 
    // Summing the x coordinates
    var resx = x1 + x2 + x3;
 
    // Summing the y coordinates
    var resy = y1 + y2 + y3;
 
    // Summing the z coordinates
    var resz = z1 + z2 + z3;
 
    // Checking the condition for equilibrium
    if (resx == 0 & resy == 0 & resz == 0)
        return true;
    else
        return false;
}
     
// Driver Code
var x1 = -2, y1 = -7, z1 = -9,
    x2 = 5, y2 = -14, z2 = 14,
    x3 = -3, y3 = 21, z3 = -5;
 
// Checking for equlibrium
if (checkEqulibrium(x1, y1, z1, x2, y2,
                    z2, x3, y3, z3))
    document.write("The vectors are at equilibrium.");
else
    document.write("The vectors are not at equilibrium.");
 
// This code is contributed by Kirti
 
</script>
Output: 
The vectors are at equilibrium.

 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

My Personal Notes arrow_drop_up
Recommended Articles
Page :