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 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
// Java program to check the equilibrium of three vectorspublic 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
# 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#
// 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// PHP program to check the equilibrium // of three vectors // Function to check the equilibrium // of three vectors function 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; $z3 = -5; // Checking for equilibrium if (checkEquilibrium($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?> |
Javascript
<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> |
Output:
The vectors are at equilibrium.
Time Complexity: O(1)
Auxiliary Space: O(1)
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