检查三条直线是否重合

原文:https://www . geesforgeks . org/check-三条直线-并发-非/

给定三线方程， a1x+b1y+c1= 0 a2T14】x+b2T18】y+c2= 0 a3T25】x 如果三条直线通过一个点，即它们在一个点相遇，则称它们是重合的。 示例:

Input : a1 = 2, b1 = -3, c1 = 5
        a2 = 3, b2 = 4, c2 = -7
        a3 = 9, b3 = -5, c3 = 8
Output : Yes

Input : a1 = 2, b1 = -3, c1 = 5
        a2 = 3, b2 = 4, c2 = -7
        a3 = 9, b3 = -5, c3 = 4
Output : No

让 a1x+b1y+c1= 0……(1) a2x+b2y+c2= 0……(2) a3x+b3y+c3= 0……(3) 假设方程(I)和(ii)相交于(x 1 ，y 1 。那么(x 1 ，y 1 将满足这两个方程。 因此，用交叉乘法的方法求解(I)和(ii)，我们得到: (x1/b1c2–b2c1)=(y1/c1a2–c2a1)=(1/a1 x1=(b1c2–b2c1/a1b2–a2b1 以及 y1=(c1a2–c2a1/a1b2–a2b1)、a 1 b = 0 因此，线(I)和(ii)交点所需坐标为 (b1c2–b2c1/a1b2a2b c1a2–c2a1/a1b2–a2b1) 对于，三条线同时进行，(x 1 ，y 所以， a3x+b3y+c3= 0 =>a3(b1c2–b2c1/a1 +b3(c1a2–c2a1/a1b2a2b1)+c3【T194 +b3(c1a2–c2a1)+c3(a1b2–a2b1【T225 以下是本办法的实施:

C++

// CPP Program to check if three straight
// line are concurrent or not
#include <bits/stdc++.h>
using namespace std;

// Return true if three line are concurrent,
// else false.
bool checkConcurrent(int a1, int b1, int c1,
                      int a2, int b2, int c2,
                      int a3, int b3, int c3)
{
    return (a3 * (b1 * c2 - b2 * c1) +
            b3 * (c1 * a2 - c2 * a1) + 
            c3 * (a1 * b2 - a2 * b1) == 0);
}

// Driven Program
int main()
{
    int a1 = 2, b1 = -3, c1 = 5;
    int a2 = 3, b2 = 4, c2 = -7;
    int a3 = 9, b3 = -5, c3 = 8;

    (checkConcurrent(a1, b1, c1, a2, b2, c2,
     a3, b3, c3) ? (cout << "Yes") : (cout << "No"));
    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java Program to check if three straight
// line are concurrent or no
import java.io.*;

class GFG {

    // Return true if three line are concurrent,
    // else false.
    static boolean checkConcurrent(int a1, int b1,
                   int c1, int a2, int b2, int c2,
                           int a3, int b3, int c3)
    {
        return (a3 * (b1 * c2 - b2 * c1) +
                b3 * (c1 * a2 - c2 * a1) +
                c3 * (a1 * b2 - a2 * b1) == 0);
    }

    // Driven Program
    public static void main (String[] args)
    {
        int a1 = 2, b1 = -3, c1 = 5;
        int a2 = 3, b2 = 4, c2 = -7;
        int a3 = 9, b3 = -5, c3 = 8;

        if(checkConcurrent(a1, b1, c1, a2, b2,
                               c2, a3, b3, c3))
            System.out.println( "Yes");
        else
            System.out.println( "No");
    }
}

// This code is contributed by anuj_67.

Python 3

# Python3 Program to check if three straight
# line are concurrent or not

# Return true if three line are concurrent,
# else false.
def checkConcurrent(a1, b1, c1, a2, b2, c2,
                                 a3, b3, c3):

    return (a3 * (b1 * c2 - b2 * c1) +
            b3 * (c1 * a2 - c2 * a1) +
            c3 * (a1 * b2 - a2 * b1) == 0)

# Driven Program
a1 = 2
b1 = -3
c1 = 5
a2 = 3
b2 = 4
c2 = -7
a3 = 9
b3 = -5
c3 = 8

if(checkConcurrent(a1, b1, c1, a2, b2, c2,
                               a3, b3, c3)):
    print("Yes")
else:
    print("No")

# This code is contributed by Smitha

C

// C# Program to check if three straight
// line are concurrent or no
using System;

class GFG {

    // Return true if three line are concurrent,
    // else false.
    static bool checkConcurrent(int a1, int b1,
                int c1, int a2, int b2, int c2,
                        int a3, int b3, int c3)
    {
        return (a3 * (b1 * c2 - b2 * c1) +
                b3 * (c1 * a2 - c2 * a1) +
                c3 * (a1 * b2 - a2 * b1) == 0);
    }

    // Driven Program
    public static void Main ()
    {
        int a1 = 2, b1 = -3, c1 = 5;
        int a2 = 3, b2 = 4, c2 = -7;
        int a3 = 9, b3 = -5, c3 = 8;

        if(checkConcurrent(a1, b1, c1, a2, b2,
                            c2, a3, b3, c3))
            Console.WriteLine( "Yes");
        else
            Console.WriteLine( "No");
    }
}

// This code is contributed by anuj_67.

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP Program to check if three straight
// line are concurrent or not

// Return true if three line are
// concurrent, else false.
function checkConcurrent($a1, $b1, $c1,
                         $a2, $b2, $c2,
                         $a3, $b3, $c3)
{
    return ($a3 * ($b1 * $c2 - $b2 * $c1) +
            $b3 * ($c1 * $a2 - $c2 * $a1) +
            $c3 * ($a1 * $b2 - $a2 * $b1) == 0);
}  

    // Driver Code
    $a1 = 2; $b1 = -3; $c1 = 5;
    $a2 = 3; $b2 = 4; $c2 = -7;
    $a3 = 9; $b3 = -5; $c3 = 8;

    if(checkConcurrent($a1, $b1, $c1, $a2, $b2,
                           $c2, $a3, $b3, $c3))
        echo "Yes";
    else
        echo "No";

// This code is contributed by anuj_67.
?>

java 描述语言

<script>

// Javascript Program to check if three straight
// line are concurrent or not

// Return true if three line are concurrent,
// else false.
function checkConcurrent( a1,  b1,  c1,
                       a2,  b2,  c2,
                       a3,  b3,  c3)
{
    return (a3 * (b1 * c2 - b2 * c1) +
            b3 * (c1 * a2 - c2 * a1) + 
            c3 * (a1 * b2 - a2 * b1) == 0);
}

// Driven Program
a1 = 2, b1 = -3, c1 = 5;
a2 = 3, b2 = 4, c2 = -7;
a3 = 9, b3 = -5, c3 = 8;
(checkConcurrent(a1, b1, c1, a2, b2, c2,
 a3, b3, c3) ? (document.write( "Yes")) : (document.write( "No")));

</script>

Output: 

Yes

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