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# Program to calculate distance between two points in 3 D

Given two coordinates (x1, y1, z1) and (x2, y2, z2) in 3 dimension. The task is to find the distance between them.
Examples :

Input: x1, y1, z1 = (2, -5, 7)
x2, y2, z1 = (3, 4, 5)
Output: 9.2736184955

Input: x1, y1, z1 = (0, 0, 0)
x2, y2, z1 = (1, 1, 1)
Output: 1.73205080757

Approach: The formula for distance between two points in 3 dimension i.e (x1, y1, z1) and (x2, y2, z2) has been derived from Pythagorean theorem which is:
Distance =
Below is the implementation of above formulae:

## C++

 // C++ program to find  // distance between // two points in 3 D. #include  #include  #include  #include  using namespace std;   // function to print distance void distance(float x1, float y1,              float z1, float x2,              float y2, float z2) {     float d = sqrt(pow(x2 - x1, 2) +                  pow(y2 - y1, 2) +                  pow(z2 - z1, 2) * 1.0);     std::cout << std::fixed;     std::cout << std::setprecision(2);     cout << " Distance is " << d;     return; }   // Driver Code int main() {     float x1 = 2;     float y1 = -5;     float z1 = 7;     float x2 = 3;     float y2 = 4;     float z2 = 5;           // function call for distance     distance(x1, y1, z1,              x2, y2, z2);     return 0; }   // This code is contributed  // by Amber_Saxena.

## C

 // C program to find  // distance between // two points in 3 D. #include  #include   // function to print distance void distance(float x1, float y1,                float z1, float x2,                float y2, float z2) {     float d = sqrt(pow(x2 - x1, 2) +                     pow(y2 - y1, 2) +                     pow(z2 - z1, 2) * 1.0);     printf("Distance is %f", d);     return; }   // Driver Code int main() {     float x1 = 2;     float y1 = -5;     float z1 = 7;     float x2 = 3;     float y2 = 4;     float z2 = 5;           // function call for distance     distance(x1, y1, z1,                  x2, y2, z2);     return 0; }   // This code is contributed  // by Amber_Saxena.

## Java

 // Java program to find  // distance between // two points in 3 D. import java .io.*; import java.lang.Math;   class GFG {       // Function for // distance  static void distance(float x1, float y1,                       float z1, float x2,                       float y2, float z2) {           double d = Math.pow((Math.pow(x2 - x1, 2) +                           Math.pow(y2 - y1, 2) +                           Math.pow(z2 - z1, 2) *                                      1.0), 0.5);     System.out.println("Distance is "+ d);     return; }   // Driver code public static void main(String[] args) {     float x1 = 2;     float y1 = -5;     float z1 = 7;     float x2 = 3;     float y2 = 4;     float z2 = 5;           // function call      // for distance     distance(x1, y1, z1,               x2, y2, z2); } }   // This code is contributed  // by Amber_Saxena.

## Python

 # Python program to find distance between # two points in 3 D.   import math   # Function to find distance def distance(x1, y1, z1, x2, y2, z2):             d = math.sqrt(math.pow(x2 - x1, 2) +                 math.pow(y2 - y1, 2) +                 math.pow(z2 - z1, 2)* 1.0)     print("Distance is ")     print(d)   # Driver Code  x1 = 2 y1 = -5 z1 = 7 x2 = 3 y2 = 4 z2 = 5   # function call for distance distance(x1, y1, z1, x2, y2, z2)

## C#

 // C# program to find  // distance between // two points in 3 D. using System;   class GFG {       // Function for // distance  static void distance(float x1, float y1,                       float z1, float x2,                       float y2, float z2) {     double d = Math.Pow((Math.Pow(x2 - x1, 2) +                           Math.Pow(y2 - y1, 2) +                           Math.Pow(z2 - z1, 2) *                                     1.0), 0.5);     Console.WriteLine("Distance is \n" + d);     return; }   // Driver code public static void Main() {     float x1 = 2;     float y1 = -5;     float z1 = 7;     float x2 = 3;     float y2 = 4;     float z2 = 5;           // function call      // for distance     distance(x1, y1, z1,               x2, y2, z2); } }   // This code is contributed  // by chandan_jnu.

## PHP

 

## Javascript

 

Output:

Distance is
9.2736184955

Time complexity: O(logn) as the inbuilt pow and sqrt function takes logarithmic time to complete all the operations hence the overall time taken by the algorithm is logarithmic.

Auxiliary Space: O(1) since no extra array is used so the space taken by the algorithm is constant

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