Check if the given vectors are at equilibrium or not - GeeksforGeeks

08 Sep, 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++
Java
Python 3
C#
PHP
Javascript
// CPP program to check the equilibrium of three vectors#include <bits/stdc++.h>using namespace std; // Function to check the equilibrium of three vectorsbool checkEquilibrium(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 and resy == 0 and resz == 0)        return true;    else        return false;} // Driver codeint main(){    int x1 = -2, y1 = -7, z1 = -9, x2 = 5, y2 = -14, z2 = 14,        x3 = -3, y3 = 21, z3 = -5;     // Checking for equilibrium    if (checkEquilibrium(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 program to check the equilibrium of three vectors public class GFG {     // Function to check the equilibrium of three vectors    static boolean checkEquilibrium(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 equilibrium                if (checkEquilibrium(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 program to check the# equilibrium of three vectors # Function to check the equilibrium# of three vectorsdef checkEquilibrium(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 equilibrium    if (resx == 0 and resy == 0 and                      resz == 0):        return True    else:        return False # Driver codex1 = -2; y1 = -7; z1 = -9x2 = 5; y2 = -14; z2 = 14x3 = -3; y3 = 21; z3 = -5 # Checking for equilibriumif (checkEquilibrium(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# program to check the equilibrium// of three vectorsclass GFG{ // Function to check the equilibrium// of three vectorsstatic bool checkEquilibrium(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 codepublic static void Main(){    int x1 = -2, y1 = -7, z1 = -9,        x2 = 5, y2 = -14, z2 = 14,        x3 = -3, y3 = 21, z3 = -5;     // Checking for equilibrium    if (checkEquilibrium(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 program to check the equilibrium// of three vectors // Function to check the equilibrium// of three vectorsfunction checkEquilibrium($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 + $z3;     // Checking the condition    // for equilibrium    if ($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; $z3 = -5; // Checking for equilibriumif (checkEquilibrium($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?>
<script> // Javascript program to check the// equilibrium of three vectors // Function to check the equilibrium// of three vectorsfunction checkEquilibrium(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 Codevar x1 = -2, y1 = -7, z1 = -9,    x2 = 5, y2 = -14, z2 = 14,    x3 = -3, y3 = 21, z3 = -5; // Checking for equilibriumif (checkEquilibrium(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>
The vectors are at equilibrium.
 
ankthon
Mithun Kumar
jit_t
Akanksha_Rai
Kirti_Mangal
avtarkumar719
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