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.
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++
#include <bits/stdc++.h>
using namespace std;
bool checkEquilibrium( int x1, int y1, int z1, int x2, int y2,
int z2, int x3, int y3, int z3)
{
int resx = x1 + x2 + x3;
int resy = y1 + y2 + y3;
int resz = z1 + z2 + z3;
if (resx == 0 and resy == 0 and resz == 0)
return true ;
else
return false ;
}
int main()
{
int x1 = -2, y1 = -7, z1 = -9, x2 = 5, y2 = -14, z2 = 14,
x3 = -3, y3 = 21, z3 = -5;
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
public class GFG {
static boolean checkEquilibrium( int x1, int y1, int z1, int x2, int y2,
int z2, int x3, int y3, int z3)
{
int resx = x1 + x2 + x3;
int resy = y1 + y2 + y3;
int resz = z1 + z2 + z3;
if (resx == 0 & resy == 0 & resz == 0 )
return true ;
else
return false ;
}
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 ;
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." );
}
}
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Python 3
def checkEquilibrium(x1, y1, z1, x2, y2,
z2, x3, y3, z3) :
resx = x1 + x2 + x3
resy = y1 + y2 + y3
resz = z1 + z2 + z3
if (resx = = 0 and resy = = 0 and
resz = = 0 ):
return True
else :
return False
x1 = - 2 ; y1 = - 7 ; z1 = - 9
x2 = 5 ; y2 = - 14 ; z2 = 14
x3 = - 3 ; y3 = 21 ; z3 = - 5
if (checkEquilibrium(x1, y1, z1,
x2, y2, z2,
x3, y3, z3)):
print ( "The vectors are at equilibrium." )
else :
print ( "The vectors are not at equilibrium." )
|
C#
class GFG
{
static bool checkEquilibrium( int x1, int y1, int z1,
int x2, int y2, int z2,
int x3, int y3, int z3)
{
int resx = x1 + x2 + x3;
int resy = y1 + y2 + y3;
int resz = z1 + z2 + z3;
if (resx == 0 & resy == 0 & resz == 0)
return true ;
else
return false ;
}
public static void Main()
{
int x1 = -2, y1 = -7, z1 = -9,
x2 = 5, y2 = -14, z2 = 14,
x3 = -3, y3 = 21, z3 = -5;
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." );
}
}
|
PHP
<?php
function checkEquilibrium( $x1 , $y1 , $z1 ,
$x2 , $y2 , $z2 ,
$x3 , $y3 , $z3 )
{
$resx = $x1 + $x2 + $x3 ;
$resy = $y1 + $y2 + $y3 ;
$resz = $z1 + $z2 + $z3 ;
if ( $resx == 0 and $resy == 0 and
$resz == 0)
return true;
else
return false;
}
$x1 = -2; $y1 = -7; $z1 = -9;
$x2 = 5; $y2 = -14; $z2 = 14;
$x3 = -3; $y3 = 21; $z3 = -5;
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." ;
?>
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Javascript
<script>
function checkEquilibrium(x1, y1, z1, x2, y2,
z2, x3, y3, z3)
{
var resx = x1 + x2 + x3;
var resy = y1 + y2 + y3;
var resz = z1 + z2 + z3;
if (resx == 0 & resy == 0 & resz == 0)
return true ;
else
return false ;
}
var x1 = -2, y1 = -7, z1 = -9,
x2 = 5, y2 = -14, z2 = 14,
x3 = -3, y3 = 21, z3 = -5;
if (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." );
</script>
|
Output:
The vectors are at equilibrium.
Time Complexity: O(1)
Auxiliary Space: O(1)
Last Updated :
25 Aug, 2022
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