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 = 17.3205081Input:

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)*k

Then area =

## C++

`// 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 Code` `int` `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 parallelogram` `def` `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 function` `def` `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 given` `using` `System;` `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 ()` `{` ` ` `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` `// PHP code to calculate area of` `// parallelogram if vectors of` `// 2 adjacent sides are given` `// Function to calculate area` `// of parallelogram` `function` `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` `?>` |

## Javascript

`<script>` `// Javascript code to calculate area of` `// parallelogram if vectors of` `// 2 adjacent sides are given` `// Function to calculate area` `// of parallelogram` `function` `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 Code` `let 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>` |

**Output:**

Area = 17.320508075688775

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend live classes with industry experts, please refer **DSA Live Classes**