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Find area of triangle if two vectors of two adjacent sides are given
• Last Updated : 16 Mar, 2021

Given two vectors in form of (xi+yj+zk) of two adjacent sides of a triangle. The task is to find out the area of a triangle.
Examples:

Input:
x1 = -2, y1 = 0, z1 = -5
x2 = 1, y2 = -2, z2 = -1
Output: Area = 6.422616289332565
Input:
x1 = -2, y1 = 1, z1 = 5
x2 = 1, y2 = 3, z2 = -1
Output: Area = 8.860022573334675 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 triangle is given by :

Area of triangle = (magnitude of cross product of vectors a and b) / 2 i.e |axb| / 2
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++ program to calculate area of // triangle if vectors of// 2 adjacent sides are given #includeusing namespace std ; // function to calculate area of triangle float area(int x1, int y1, int z1, int x2, int y2, int z2){    float area = sqrt(pow((y1 * z2 - y2 * z1),2)             + pow((x1 * z2 - x2 * z1),2) +               pow((x1 * y2 - x2 * y1),2)) ;              area = area / 2;    return area ;     }     // Driver Codeint main(){    int    x1 = -2 ;    int y1 = 0 ;    int z1 = -5 ;    int x2 = 1 ;    int y2 = -2 ;    int z2 = -1 ;    float  a = area(x1, y1, z1, x2, y2, z2) ;     cout << "Area = " << a << endl;                             return 0;// This code is contributed by ANKITRAI1}

## Java

 // Java program to calculate area of// triangle if vectors of// 2 adjacent sides are givenimport java.util.*; class solution{// function to calculate area of trianglestatic float area(int x1, int y1, int z1, int x2, int y2, int z2){  double a =Math.pow((y1 * z2 - y2 * z1),2)            + Math.pow((x1 * z2 - x2 * z1),2) +                Math.pow((x1 * y2 - x2 * y1),2);float area = (float)Math.sqrt(a) ;         area = area / 2;    return area ;} //Driver programpublic static void main(String arr[]){    int x1 = -2 ;    int y1 = 0 ;    int z1 = -5 ;    int x2 = 1 ;    int y2 = -2 ;    int z2 = -1 ;    float a = area(x1, y1, z1, x2, y2, z2) ;    System.out.println("Area= "+a);} }//This code is contributed by//Surendra_Gangwar

## Python 3

 # Python code to calculate area of# triangle if vectors of# 2 adjacent sides are givenimport math # to calculate area of triangledef 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)    area = area / 2    return area # main functiondef main():    x1 = -2    y1 = 0    z1 = -5    x2 = 1    y2 = -2    z2 = -1    a = area(x1, y1, z1, x2, y2, z2)    print("Area = ", a) # driver code   if __name__=="__main__":    main()

## C#

 // C# program to calculate area // of triangle if vectors of// 2 adjacent sides are givenusing System;class GFG{// function to calculate area of trianglestatic float area(int x1, int y1, int z1,                  int x2, int y2, int z2){double a = Math.Pow((y1 * z2 - y2 * z1), 2) +           Math.Pow((x1 * z2 - x2 * z1), 2) +           Math.Pow((x1 * y2 - x2 * y1), 2);float area = (float)Math.Sqrt(a) ;         area = area / 2;    return area ;} // Driver Codepublic static void Main(){    int x1 = -2;    int y1 = 0;    int z1 = -5;    int x2 = 1;    int y2 = -2;    int z2 = -1;    float a = area(x1, y1, z1, x2, y2, z2);    Console.WriteLine("Area = " + a);}} // This code is contributed// by inder_verma

## PHP

 

## Javascript

 
Output:
Area =  6.422616289332565

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