Program to calculate angle between two N-Dimensional vectors
Given an array arr[] consisting of magnitudes of two N-Dimensional vectors A and B, the task is to find the angle between the two vectors.
Examples:
Input: arr[] = {-0.5, -2, 1}, brr[] = {-1, -1, -0.3}
Output: 0.845289
Explanation:
Placing the values in the formula, the required result is obtained.
Input: arr[] = {1, -2, 3}, brr[] = {2, 3, -1}
Output: -0.5
Approach: The idea is based on the mathematical formula of finding the dot product of two vectors and dividing it by the product of the magnitude of vectors A, B.
Formula:
Considering the two vectors to be separated by angle θ. the dot product of the two vectors is given by the equation:
Therefore,
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to find the magnitude // of the given vector double magnitude( double arr[], int N) { // Stores the final magnitude double magnitude = 0; // Traverse the array for ( int i = 0; i < N; i++) magnitude += arr[i] * arr[i]; // Return square root of magnitude return sqrt (magnitude); } // Function to find the dot // product of two vectors double dotProduct( double arr[], double brr[], int N) { // Stores dot product double product = 0; // Traverse the array for ( int i = 0; i < N; i++) product = product + arr[i] * brr[i]; // Return the product return product; } void angleBetweenVectors( double arr[], double brr[], int N) { // Stores dot product of two vectors double dotProductOfVectors = dotProduct(arr, brr, N); // Stores magnitude of vector A double magnitudeOfA = magnitude(arr, N); // Stores magnitude of vector B double magnitudeOfB = magnitude(brr, N); // Stores angle between given vectors double angle = dotProductOfVectors / (magnitudeOfA * magnitudeOfB); // Print the angle cout << angle; } // Driver Code int main() { // Given magnitude arrays double arr[] = { -0.5, -2, 1 }; double brr[] = { -1, -1, 0.3 }; // Size of the array int N = sizeof (arr) / sizeof (arr[0]); // Function call to find the // angle between two vectors angleBetweenVectors(arr, brr, N); return 0; } |
Java
// Java program for the above approach class GFG{ // Function to find the magnitude // of the given vector static double magnitude( double arr[], int N) { // Stores the final magnitude double magnitude = 0 ; // Traverse the array for ( int i = 0 ; i < N; i++) magnitude += arr[i] * arr[i]; // Return square root of magnitude return Math.sqrt(magnitude); } // Function to find the dot // product of two vectors static double dotProduct( double [] arr, double [] brr, int N) { // Stores dot product double product = 0 ; // Traverse the array for ( int i = 0 ; i < N; i++) product = product + arr[i] * brr[i]; // Return the product return product; } static void angleBetweenVectors( double [] arr, double [] brr, int N) { // Stores dot product of two vectors double dotProductOfVectors = dotProduct(arr, brr, N); // Stores magnitude of vector A double magnitudeOfA = magnitude(arr, N); // Stores magnitude of vector B double magnitudeOfB = magnitude(brr, N); // Stores angle between given vectors double angle = dotProductOfVectors / (magnitudeOfA * magnitudeOfB); // Print the angle System.out.println(angle); } // Driver Code public static void main(String[] args) { // Given magnitude arrays double [] arr = { - 0.5 , - 2 , 1 }; double [] brr = { - 1 , - 1 , 0.3 }; // Size of the array int N = arr.length; // Function call to find the // angle between two vectors angleBetweenVectors(arr, brr, N); } } // This code is contributed by user_qa7r |
Python3
# Python3 program for the above approach import math # Function to find the magnitude # of the given vector def magnitude(arr, N): # Stores the final magnitude magnitude = 0 # Traverse the array for i in range (N): magnitude + = arr[i] * arr[i] # Return square root of magnitude return math.sqrt(magnitude) # Function to find the dot # product of two vectors def dotProduct(arr, brr, N): # Stores dot product product = 0 # Traverse the array for i in range (N): product = product + arr[i] * brr[i] # Return the product return product def angleBetweenVectors(arr, brr, N): # Stores dot product of two vectors dotProductOfVectors = dotProduct(arr, brr, N) # Stores magnitude of vector A magnitudeOfA = magnitude(arr, N) # Stores magnitude of vector B magnitudeOfB = magnitude(brr, N) # Stores angle between given vectors angle = (dotProductOfVectors / (magnitudeOfA * magnitudeOfB)) # Print the angle print ( '%.5f' % angle) # Driver Code if __name__ = = "__main__" : # Given magnitude arrays arr = [ - 0.5 , - 2 , 1 ] brr = [ - 1 , - 1 , 0.3 ] # Size of the array N = len (arr) # Function call to find the # angle between two vectors angleBetweenVectors(arr, brr, N) # This code is contributed by ukasp. |
C#
// C# program for the above approach using System; using System.Collections.Generic; class GFG{ // Function to find the magnitude // of the given vector static double magnitude( double []arr, int N) { // Stores the final magnitude double magnitude = 0; // Traverse the array for ( int i = 0; i < N; i++) magnitude += arr[i] * arr[i]; // Return square root of magnitude return Math.Sqrt(magnitude); } // Function to find the dot // product of two vectors static double dotProduct( double []arr, double []brr, int N) { // Stores dot product double product = 0; // Traverse the array for ( int i = 0; i < N; i++) product = product + arr[i] * brr[i]; // Return the product return product; } static void angleBetweenVectors( double []arr, double []brr, int N) { // Stores dot product of two vectors double dotProductOfVectors = dotProduct(arr, brr, N); // Stores magnitude of vector A double magnitudeOfA = magnitude(arr, N); // Stores magnitude of vector B double magnitudeOfB = magnitude(brr, N); // Stores angle between given vectors double angle = dotProductOfVectors / (magnitudeOfA * magnitudeOfB); // Print the angle Console.Write(angle); } // Driver Code public static void Main() { // Given magnitude arrays double []arr = { -0.5, -2, 1 }; double []brr = { -1, -1, 0.3 }; // Size of the array int N = arr.Length; // Function call to find the // angle between two vectors angleBetweenVectors(arr, brr, N); } } // This code is contributed by bgangwar59 |
Javascript
<script> // Javascript program for the above approach // Function to find the magnitude // of the given vector function magnitude(arr, N) { // Stores the final magnitude var magnitude = 0; // Traverse the array for ( var i = 0; i < N; i++) magnitude += arr[i] * arr[i]; // Return square root of magnitude return Math.sqrt(magnitude); } // Function to find the dot // product of two vectors function dotProduct(arr, brr,N) { // Stores dot product var product = 0; // Traverse the array for ( var i = 0; i < N; i++) product = product + arr[i] * brr[i]; // Return the product return product; } function angleBetweenVectors(arr, brr, N) { // Stores dot product of two vectors var dotProductOfVectors = dotProduct(arr, brr, N); // Stores magnitude of vector A var magnitudeOfA = magnitude(arr, N); // Stores magnitude of vector B var magnitudeOfB = magnitude(brr, N); // Stores angle between given vectors var angle = dotProductOfVectors / (magnitudeOfA * magnitudeOfB); // Print the angle document.write( angle.toFixed(6)); } // Driver Code // Given magnitude arrays var arr = [ -0.5, -2, 1 ]; var brr = [ -1, -1, 0.3 ]; // Size of the array var N = arr.length; // Function call to find the // angle between two vectors angleBetweenVectors(arr, brr, N); </script> |
0.845289
Time Complexity: O(1)
Auxiliary Space: O(1)