# 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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