Check if the given vectors are at equilibrium or not

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.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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



Output:

The vectors are at equilibrium.

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