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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 ``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

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## Javascript

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Output:
`The vectors are at equilibrium.`

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