Program for dot product and cross product of two vectors

04 Jun, 2022
There are two vector A and B and we have to find the dot product and cross product of two vector array. Dot product is also known as scalar product and cross product also known as vector product.Dot Product – Let we have given two vector A = a1 * i + a2 * j + a3 * k and B = b1 * i + b2 * j + b3 * k. Where i, j and k are the unit vector along the x, y and z directions. Then dot product is calculated as dot product = a1 * b1 + a2 * b2 + a3 * b3Example –  
A = 3 * i + 5 * j + 4 * k
B = 2 * i + 7 * j + 5 * k
dot product = 3 * 2 + 5 * 7 + 4 * 5
            = 6 + 35 + 20
            = 61
Cross Product – Let we have given two vector A = a1 * i + a2 * j + a3 * k and B = b1 * i + b2 * j + b3 * k. Then cross product is calculated as cross product = (a2 * b3 – a3 * b2) * i + (a3 * b1 – a1 * b3) * j + (a1 * b2 – a2 * b1) * k, where [(a2 * b3 – a3 * b2), (a3 * b1 – a1 * b3), (a1 * b2 – a2 * b1)] are the coefficient of unit vector along i, j and k directions.Example –  
A = 3 * i + 5 * j + 4 * k
B = 2 * i + 7 * j + 5 * k
cross product 
= (5 * 5 - 4 * 7) * i 
      + (4 * 2 - 3 * 5) * j + (3 * 7 - 5 * 2) * k
= (-3)*i + (-7)*j + (11)*k
Example –  
Input: vect_A[] = {3, -5, 4}
        vect_B[] = {2, 6, 5}
Output: Dot product: -4
         Cross product = -49 -7 28
 
Code-  
C++
Java
Python3
C#
PHP
Javascript
// C++ implementation for dot product// and cross product of two vector.#include <bits/stdc++.h>#define n 3 using namespace std; // Function that return// dot product of two vector array.int dotProduct(int vect_A[], int vect_B[]){     int product = 0;     // Loop for calculate dot product    for (int i = 0; i < n; i++)         product = product + vect_A[i] * vect_B[i];    return product;} // Function to find// cross product of two vector array.void crossProduct(int vect_A[], int vect_B[], int cross_P[]) {     cross_P[0] = vect_A[1] * vect_B[2] - vect_A[2] * vect_B[1];    cross_P[1] = vect_A[2] * vect_B[0] - vect_A[0] * vect_B[2];    cross_P[2] = vect_A[0] * vect_B[1] - vect_A[1] * vect_B[0];} // Driver functionint main(){     int vect_A[] = { 3, -5, 4 };    int vect_B[] = { 2, 6, 5 };    int cross_P[n];     // dotProduct function call    cout << "Dot product:";    cout << dotProduct(vect_A, vect_B) << endl;     // crossProduct function call    cout << "Cross product:";    crossProduct(vect_A, vect_B, cross_P);     // Loop that print    // cross product of two vector array.    for (int i = 0; i < n; i++)         cout << cross_P[i] << " ";    return 0;}
// java implementation for dot product// and cross product of two vector.import java.io.*; class GFG {     static int n = 3;     // Function that return    // dot product of two vector array.    static int dotProduct(int vect_A[], int vect_B[])    {         int product = 0;         // Loop for calculate dot product        for (int i = 0; i < n; i++)            product = product + vect_A[i] * vect_B[i];        return product;    }     // Function to find    // cross product of two vector array.    static void crossProduct(int vect_A[], int vect_B[],                             int cross_P[])     {         cross_P[0] = vect_A[1] * vect_B[2]                     - vect_A[2] * vect_B[1];        cross_P[1] = vect_A[2] * vect_B[0]                     - vect_A[0] * vect_B[2];        cross_P[2] = vect_A[0] * vect_B[1]                     - vect_A[1] * vect_B[0];    }     // Driver code    public static void main(String[] args)    {        int vect_A[] = { 3, -5, 4 };        int vect_B[] = { 2, 6, 5 };        int cross_P[] = new int[n];         // dotProduct function call        System.out.print("Dot product:");        System.out.println(dotProduct(vect_A, vect_B));         // crossProduct function call        System.out.print("Cross product:");        crossProduct(vect_A, vect_B, cross_P);         // Loop that print        // cross product of two vector array.        for (int i = 0; i < n; i++)             System.out.print(cross_P[i] + " ");    }} // This code is contributed by vt_m
# Python3 implementation for dot product# and cross product of two vector. n = 3 # Function that return# dot product of two vector array.def dotProduct(vect_A, vect_B):     product = 0     # Loop for calculate dot product    for i in range(0, n):        product = product + vect_A[i] * vect_B[i]     return product # Function to find# cross product of two vector array.def crossProduct(vect_A, vect_B, cross_P):     cross_P.append(vect_A[1] * vect_B[2] - vect_A[2] * vect_B[1])    cross_P.append(vect_A[2] * vect_B[0] - vect_A[0] * vect_B[2])    cross_P.append(vect_A[0] * vect_B[1] - vect_A[1] * vect_B[0])  # Driver functionif __name__=='__main__':    vect_A = [3, -5, 4]    vect_B = [2, 6, 5]    cross_P = [] # dotProduct function call    print("Dot product:", end =" ")    print(dotProduct(vect_A, vect_B)) # crossProduct function call    print("Cross product:", end =" ")    crossProduct(vect_A, vect_B, cross_P) # Loop that print# cross product of two vector array.    for i in range(0, n):        print(cross_P[i], end =" ") # This code is contributed by# Sanjit_Prasad
// C# implementation for dot product// and cross product of two vector.using System; class GFG {     static int n = 3;     // Function that return dot    // product of two vector array.    static int dotProduct(int[] vect_A,                          int[] vect_B)    {         int product = 0;         // Loop for calculate dot product        for (int i = 0; i < n; i++)            product = product + vect_A[i] * vect_B[i];        return product;    }     // Function to find cross product    // of two vector array.    static void crossProduct(int[] vect_A,                             int[] vect_B, int[] cross_P)     {         cross_P[0] = vect_A[1] * vect_B[2]                     - vect_A[2] * vect_B[1];        cross_P[1] = vect_A[2] * vect_B[0]                     - vect_A[0] * vect_B[2];        cross_P[2] = vect_A[0] * vect_B[1]                     - vect_A[1] * vect_B[0];    }     // Driver code    public static void Main()    {        int[] vect_A = { 3, -5, 4 };        int[] vect_B = { 2, 6, 5 };        int[] cross_P = new int[n];         // dotProduct function call        Console.Write("Dot product:");         Console.WriteLine(            dotProduct(vect_A, vect_B));         // crossProduct function call        Console.Write("Cross product:");        crossProduct(vect_A, vect_B, cross_P);         // Loop that print        // cross product of two vector array.        for (int i = 0; i < n; i++)            Console.Write(cross_P[i] + " ");    }} // This code is contributed by vt_m.
<?php// PHP implementation for dot// product and cross product// of two vector.$n = 3; // Function that return// dot product of two// vector array.function dotproduct($vect_A, $vect_B){    global $n;    $product = 0;     // Loop for calculate    // dot product    for ($i = 0; $i < $n; $i++)         $product = $product + $vect_A[$i] *                            $vect_B[$i];    return $product;} // Function to find// cross product of// two vector array.function crossproduct($vect_A,                    $vect_B, $cross_P) {     $cross_P[0] = $vect_A[1] * $vect_B[2] -                $vect_A[2] * $vect_B[1];    $cross_P[1] = $vect_A[2] * $vect_B[0] -                $vect_A[0] * $vect_B[2];    $cross_P[2] = $vect_A[0] * $vect_B[1] -                $vect_A[1] * $vect_B[0];    return $cross_P;} // Driver Code$vect_A = array( 3, -5, 4 );$vect_B = array( 2, 6, 5 );$cross_P = array_fill(0, $n, 0); // dotproduct function callecho "Dot product:";echo dotproduct($vect_A, $vect_B); // crossproduct function callecho "\nCross product:";$cross_P = crossproduct($vect_A,                        $vect_B,                        $cross_P); // Loop that print// cross product of// two vector array.for ($i = 0; $i < $n; $i++)     echo $cross_P[$i] . " "; // This code is contributed by mits?>
<script> // Javascript implementation for dot product// and cross product of two vector. let n = 3;       // Function that return    // dot product of two vector array.    function dotProduct(vect_A, vect_B)    {           let product = 0;           // Loop for calculate dot product        for (let i = 0; i < n; i++)            product = product + vect_A[i] * vect_B[i];        return product;    }       // Function to find    // cross product of two vector array.    function crossProduct(vect_A, vect_B,                             cross_P)       {           cross_P[0] = vect_A[1] * vect_B[2]                     - vect_A[2] * vect_B[1];        cross_P[1] = vect_A[2] * vect_B[0]                     - vect_A[0] * vect_B[2];        cross_P[2] = vect_A[0] * vect_B[1]                     - vect_A[1] * vect_B[0];    }     // Driver code         let vect_A = [ 3, -5, 4 ];        let vect_B = [ 2, 6, 5 ];        let cross_P = [];           // dotProduct function call        document.write("Dot product:");        document.write(dotProduct(vect_A, vect_B) + "<br/>");           // crossProduct function call        document.write("Cross product:");        crossProduct(vect_A, vect_B, cross_P);           // Loop that print        // cross product of two vector array.        for (let i = 0; i < n; i++)               document.write(cross_P[i] + " ");                    // This code is contributed by sanjoy_62.            </script>
Dot product:-4
Cross product:-49 -7 28
 
Time Complexity: O(3), the code will run in a constant time because the size of the arrays will be always 3.Auxiliary Space: O(3), no extra space is required, so it is a constant. 
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