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Find area of parallelogram if vectors of two adjacent sides are given
• Last Updated : 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 = 4
Output: Area = 17.3205081
Input:
x1 = 1, y1 = 3, z1 = 2
x2 = 1, y2 = -3, z2 = 4
Output: 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)*k
Then area = ## C++

 // C++ code to calculate area of// parallelogram if vectors of// 2 adjacent sides are given #includeusing 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

 // 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

 # 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#

 // 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

 

## Javascript

 
Output:
Area =  17.320508075688775

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