Given three direction cosines l, m and n of a 3-D plane, the task is to check if it is possible to draw a straight line with them or not. Print Yes if possible else print No.
Examples:
Input: l = 0.258, m = 0.80, n = 0.23
Output: NoInput: l = 0.70710678, m = 0.5, n = 0.5
Output: Yes
Approach: If a straight line forms angle a with positive X-axis, angle b with positive Y-axis and angle c with positive Z-axis then its direction cosines are cos(a), cos(b) and cos(c).
For a straight line, cos2(a) + cos2(b) + cos2(c) = 1.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function that returns true// if a straight line is possiblebool isPossible(float x, float y, float z){ float a = x * x + y * y + z * z; if (ceil(a) == 1 && floor(a) == 1) return true; return false;}// Driver codeint main(){ float l = 0.70710678, m = 0.5, n = 0.5; if (isPossible(l, m, n)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java implementation of the approachimport java.util.*;class GFG{// Function that returns true// if a straight line is possiblestatic boolean isPossible(float x, float y, float z){ float a = x * x + y * y + z * z; if (Math.ceil(a) == 1 && Math.floor(a) == 1) return true; return false;}// Driver codepublic static void main(String args[]){ float l = 0.70710678f, m = 0.5f, n = 0.5f; if (isPossible(l, m, n)) System.out.println("Yes"); else System.out.println("No");}}// This code is contributed by// Shashank_Sharma |
Python3
# Python3 implementation of the approach from math import ceil, floor# Function that returns true # if a straight line is possible def isPossible(x, y, z) : a = x * x + y * y + z * z a = round(a, 8) if (ceil(a) == 1 & floor(a) == 1) : return True return False# Driver code if __name__ == "__main__" : l = 0.70710678 m = 0.5 n = 0.5 if (isPossible(l, m, n)): print("Yes") else : print("No")# This code is contributed by Ryuga |
C#
// C# implementation of the approachusing System;class GFG{// Function that returns true// if a straight line is possiblestatic bool isPossible(float x, float y, float z){ float a = x * x + y * y + z * z; if (Math.Ceiling(a) == 1 && Math.Floor(a) == 1) return true; return false;}// Driver codepublic static void Main(){ float l = 0.70710678f, m = 0.5f, n = 0.5f; if (isPossible(l, m, n)) Console.WriteLine("Yes"); else Console.WriteLine("No");}}// This code is contributed by Ita_c. |
PHP
<?php// PHP implementation of the approach// Function that returns true// if a straight line is possiblefunction isPossible($x, $y, $z){ $a = round($x * $x + $y * $y + $z * $z); if (ceil($a) == 1 && floor($a) == 1) return true; return false;}// Driver code$l = 0.70710678; $m = 0.5; $n = 0.5;if (isPossible($l, $m, $n)) echo("Yes");else echo("No");// This code is contributed by mukul singh. |
Javascript
<script>// Javascript implementation of the approach// Function that returns true// if a straight line is possiblefunction isPossible(x,y,z){ let a = Math.round(x * x + y * y + z * z); if (Math.ceil(a) == 1 && Math.floor(a) == 1) return true; return false;}// Driver codelet l = 0.70710678, m = 0.5, n = 0.5;if (isPossible(l, m, n)) document.write("Yes");else document.write("No");// This code is contributed by rag2127</script> |
Output:
Yes
Time Complexity: O(1)
Auxiliary Space: O(1)
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