Find area of parallelogram if vectors of two adjacent sides are given - GeeksforGeeks

14 Apr, 2021
Given two vectors in form of (xi+yj+zk) of two adjacent sides of a parallelogram. The task is to find out the area of a parallelogram.Example:  
Input: x1 = 3, y1 = 1, z1 = -2 x2 = 1, y2 = -3, z2 = 4Output: Area = 17.3205081 Input: x1 = 1, y1 = 3, z1 = 2 x2 = 1, y2 = -3, z2 = 4Output: Area = 19.078784028338912 
 
 
Approach: Suppose we have two vectors a(x1*i+y1*j+z1*k) and b(x2*i+y2*j+z2*k) and we know that area of parallelogram is given by :  
Area of parallelogram = magnitude of cross product of vectors a and b i.e |axb| And we know a X b = (y1*z2 – y2*z1)*i – (x1*z2 – x2*z1)*j + (x1*y2 – x2*y1)*kThen area = 
 
C++
Java
Python
C#
PHP
Javascript
// C++ code to calculate area of// parallelogram if vectors of// 2 adjacent sides are given #include<bits/stdc++.h>using namespace std ; // Function to calculate area of parallelogram float area(float x1, float y1, float z1, float x2,            float y2, float z2)    {        float area = sqrt(pow((y1 * z2 - y2 * z1),2)                        + pow((x1 * z2 - x2 * z1),2) +                         pow((x1 * y2 - x2 * y1),2));        return area;    }     // Driver Codeint main(){    float x1 = 3;    float y1 = 1;    float z1 = -2;    float x2 = 1;    float y2 = -3;    float z2 = 4;    float a = area(x1, y1, z1, x2, y2, z2);    cout << "Area = " << a;    return 0;// This code is contributed// by Amber_Saxena.}
// Java code to calculate area of // parallelogram if vectors of// 2 adjacent sides are given public class GFG {         // Function to calculate area of parallelogram      static float area(float x1, float y1, float z1, float x2,                float y2, float z2)        {             float area =(float) Math.sqrt(Math.pow((y1 * z2 - y2 * z1),2)                            + Math.pow((x1 * z2 - x2 * z1),2) +                             Math.pow((x1 * y2 - x2 * y1),2));            return area;        }      // Driver code    public static void main (String args[]){         float x1 = 3;            float y1 = 1;            float z1 = -2;            float x2 = 1;            float y2 = -3;            float z2 = 4;            float a = area(x1, y1, z1, x2, y2, z2);            System.out.println("Area = " + a) ;               } // This code is contributed by ANKITRAI1}
# Python code to calculate area of# parallelogram if vectors of# 2 adjacent sides are given import math # to calculate area of parallelogramdef area(x1, y1, z1, x2, y2, z2):    area = math.sqrt((y1 * z2 - y2 * z1) ** 2           + (x1 * z2 - x2 * z1) ** 2 +           (x1 * y2 - x2 * y1) ** 2)    return area # main functiondef main():    x1 = 3    y1 = 1    z1 = -2    x2 = 1    y2 = -3    z2 = 4    a = area(x1, y1, z1, x2, y2, z2)    print("Area = ", a) # driver code   if __name__=="__main__":    main()
// C# code to calculate area of// parallelogram if vectors of// 2 adjacent sides are givenusing System; class GFG{ // Function to calculate area// of parallelogramstatic float area(float x1, float y1,                  float z1, float x2,                  float y2, float z2){    float area = (float) Math.Sqrt(Math.Pow((y1 * z2 - y2 * z1), 2) +                                   Math.Pow((x1 * z2 - x2 * z1), 2) +                                   Math.Pow((x1 * y2 - x2 * y1), 2));    return area;} // Driver codepublic static void Main (){    float x1 = 3;    float y1 = 1;    float z1 = -2;    float x2 = 1;    float y2 = -3;    float z2 = 4;    float a = area(x1, y1, z1, x2, y2, z2);    Console.Write("Area = " + a) ;}} // This code is contributed// by ChitraNayal
<?php// PHP code to calculate area of// parallelogram if vectors of// 2 adjacent sides are given // Function to calculate area// of parallelogramfunction area($x1, $y1, $z1,              $x2, $y2, $z2){        $area = sqrt(pow(($y1 * $z2 - $y2 * $z1), 2) +                     pow(($x1 * $z2 - $x2 * $z1), 2) +                     pow(($x1 * $y2 - $x2 * $y1), 2));        return $area;}     // Driver Code$x1 = 3; $y1 = 1; $z1 = -2;$x2 = 1; $y2 = -3; $z2 = 4;$a = area($x1, $y1, $z1,          $x2, $y2, $z2);echo ("Area = ");echo ($a);     // This code is contributed// by Shivi_Aggarwal?>
<script> // Javascript code to calculate area of// parallelogram if vectors of// 2 adjacent sides are given // Function to calculate area// of parallelogramfunction area(x1, y1, z1,              x2, y2, z2){        area = Math.sqrt(Math.pow((y1 * z2 - y2 * z1), 2) +                     Math.pow((x1 * z2 - x2 * z1), 2) +                     Math.pow((x1 * y2 - x2 * y1), 2));        return area;}     // Driver Codelet x1 = 3;let y1 = 1;let z1 = -2;let x2 = 1;let y2 = -3;let z2 = 4;a = area(x1, y1, z1,          x2, y2, z2);document.write ("Area = ");document.write (a);     // This code is contributed by Bobby </script>
Area =  17.320508075688775
 
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